RL Circuit Research Articles

Design and analysis of two layers RLC network of rectangular topology by wave concept iterative process method

AbstractThe paper presents a theoretical study of a rectangular electrical network built on two layers. First, the auxiliary source notion is introduced for characterizing the potential difference over each electrical element, then the mathematical formalism of the Wave Concept Iterative Process method is developed and adopted to the studied circuit. The used method is based on the concept of the incident and reflected waves which are defined from the current and voltage at each branch of the circuit. Two relations connecting the waves are established into two definition domains: a spectral‐domain using the Kirchhoff laws and the auxiliary source connections and, another spatial defining the boundary conditions and the circuit design. Hence a two equations system is obtained and it is resolved by an iterative process, the transition between the two domains is ensured by the fast Fourier transform and its inverse. Moreover, the equivalent impedance between the feeding source and the nodes of the bottom layer has been calculated. Among the numerical simulation methods, this method has demonstrated its performances for analyzing various designs of the networks including RL, RC and RLC circuits excited by a lumped voltage source. The effect of the circuit parameters on the electrical currents and equivalent impedance has been studied.

An experimental analysis of DC magnetic blowout high-speed circuit breakers’ parameters

High-speed circuit breakers (HSCB) used in DC circuits are one of the basic elements of overload, short-circuit and electric shock protection. Such breakers are used in transport (trams, trolleybuses, subways and railways) in electric power supply facilities and in vehicles. The performance and capability of limiting the current depend on the HSCB design and solutions applied in it. The circuit parameters, particularly its inductance also affect the performance. Additionally, each DC breaking in the RL circuit is accompanied by overvoltages whose level depends on the circuit parameters and breaker design. The paper discussed the process of direct current breaking by magnetic blowout high-speed circuit breakers and factors that affect the HSCB performance, i. e. opening time and arcing time. The influence of the circuit parameters and HSCB design on the value of arc voltage is outlined. The results of laboratory tests of 4 types of high-speed circuit breakers produced in Europe are presented. The test results were used to analyze the effect of current changes in the short circuit on the time of current breaking and the value of switching overvoltages – arc voltage. The results of simulation of the short-circuit breaking in the RL DC circuit made at the rate-of-rise of current in the circuit are presented. Based on the tests and simulations, the current breaking times, values of arc voltage generated in this process and arc energy that is acquired and dissipated by the arc chamber are determined. The objective of the tests and simulations was to answer the question whether it is possible to turn off direct current quickly without generating high arc voltage values – overvoltages in the circuit and how di/dt changes should be formed by a high-speed circuit breaker to achieve the shortest possible time with the lowest possible arc voltage and its lowest energy

An Improved Algorithm for AC Impedance Extraction

The overall system stability of interconnected electrical and electronic systems is associated with the input and output impedances of each individual system, therefore, accurate AC impedance measurement for a linear and nonlinear systems are imperative. These impedances are normally measured using small-signal frequency injection techniques. However, the harmonic transfers from the output side to the input side and vice versa deteriorates the measured results, making them ambiguous. These harmonic transfers cause the problems of frequency aliasing as well as spectral leakages leading to inaccurate measurements of results. In order to achieve the precise and accurate results, there is a need to adopt such an impedance measuring technique which is the best among the available techniques. A new algorithm is proposed to modify the range of frequencies of interest and inject such small-signal frequencies which do not interfere with the system harmonics. The measurement of the AC impedance of the three-phase RL circuit utilizing three different small-signal injection techniques is performed. From the results displayed, it is clear that all the techniques perform well, therefore, the most simple, single phase line-current injection was selected for the AC impedance measurement of the nonlinear switching circuit such as six-pulse rectifier. The issues discussed above are more serious in nonlinear switching circuit because of the presence of higher order switching harmonics in the circuit. The proposed algorithm is applied to measure the output-impedance of the three-phase AC power supply as well as the AC input-impedance of the six-pulse rectifier. These results of the switch vs average model and that of average model vs. experimental prototype are displayed for comparison, and it is clear that the proposed algorithm offers much-improved results.

Comparative Study of Integer and Non-Integer Order Models of Synchronous Generator

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.

MATHEMATICAL AND STATISTICAL ANALYSIS OF RL AND RC FRACTIONAL-ORDER CIRCUITS

The RL and RC circuits are analyzed in this research paper. The classical model of these circuits is generalized using the modern concept of fractional derivative with Mittag-Leffler function in its kernel. The fractional differential equations are solved for exact solutions using the Laplace transform technique and the inverse transformation. The obtained solutions are plotted and presented in tables to show the effect of resistance, inductance and fractional parameter on current and voltage. Furthermore, the statistical analysis is presented to predict the seasonal of time and other parameters on the current flowing in the circuit. The statistical analysis shows that the variation in current is insignificant with respect to time and is more significant with respect to other parameters.

CUBE POLYGON: A NEW MODIFIED EULER METHOD TO IMPROVE ELECTRIC CIRCUIT EFFICIENCY

Euler method is a numerical order process for solving problems with the Ordinary Differential Equation (ODE). It is a fast and easy way. While Euler offers a simple procedure for solving ODEs, problems such as complexity, processing time and accuracy have driven others to use more sophisticated methods. Improvements to the Euler method have attracted much attention resulting in numerous modified Euler methods. This paper proposes Cube Polygon, a modified Euler method with improved accuracy and complexity. In order to demonstrate the accuracy and easy implementation of the proposed method, several examples are presented. Cube Polygon’s performance was compared to Polygon’s scheme and evaluated against exact solutions using SCILAB. Results indicate that not only Cube Polygon has produced solutions that are close to identical solutions for small step sizes, but also for higher step sizes, thus generating more accurate results and decrease complexity. Also known in this paper is the general of the RL circuit due to the ODE problem.

Direct Consideration of Eddy Current Losses in Laminated Magnetic Cores in Finite Element Method (FEM) Calculations Using the Laplace Transform

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.

Study of the Voltage Behavior of Jointless Superconducting 2G Loops During Pulse Magnetization

Low critical temperature superconducting coils can conduct persistent currents with almost no losses, as the technique to make joints is well developed and the resistive losses are negligible. The replacement of these superconductors by high-temperature superconductors may greatly reduce refrigeration costs. However, even though the technique for making these joints has greatly developed over the last years, there are still inherent difficulties associated to that process. Coils made with partially slit loops of high temperature superconducting tape have no joints, and therefore can conduct current in persistent mode. Since there are no terminals, its current must be induced through magnetization techniques, for instance, by the means of a transformer. The occurrence of persistent current is related to the voltage in the sample, making it interesting to study the voltage behavior for different regions of operation. In this work, a jointless 2G loop was magnetized with pulse magnetization from which the curves of voltage and current as functions of time were obtained. After several tests, it was possible to divide the superconductor behavior into three different stages of operation, depending on the current levels reached: for low current values, the material behaves as a perfect inductor; for current values near the critical current, it behaves as an RL circuit; and for higher values, resistance dependent on the temperature has to be taken into account. A direct relation between persistent current and the arise of a dissipative state was noted and the highest values of persistent current were observed when the pulse was intense enough to produce significant temperature variations in the sample.

Reduction of structural vibrations with the piezoelectric stacks ring

It is known that piezoelectric material shunted with external circuits can convert mechanical energy to electrical energy, which is so called piezoelectric shunt damping technology. In this paper, a piezoelectric stacks ring (PSR) is designed for vibration control of beams and rotor systems. A relative simple electromechanical model of an Euler Bernoulli beam supported by two piezoelectric stacks shunted with resonant RL circuits is established. The equation of motion of such simplified system has been derived using Hamilton’s principle. A more realistic FEA model is developed. The numerical analysis is carried out using COMSOL® and the simulation results show a significant reduction of vibration amplitude at the specific natural frequencies. Using finite element method, the influence of circuit parameters on lateral vibration control is discussed. A preliminary experiment of a prototype PSR verifies the PSR’s vibration reduction effect.

Dynamic similarity analysis for a piezo-electromechanical system

Most research about using piezoelectric stacks to suppress vibration of mechanical structures didn’t involve the similarity problem for the piezoelectric stacks. The goal of this paper is to investigate the dynamic similarity between a prototype piezo stack and a scaled up or down piezo stack, whilst discussing the feasibility of predicting the vibration of prototype structure which use the piezoelectric stacks for vibration control. To illustrate this problem concisely, a single-DOF system consists of a proof mass and a piezo stack shunted with a series RL circuit is considered. Firstly, the governing equation of such piezo-electromechanical system in frequency domain is derived. Next the dynamic similarity of prototype and model stack is analyzed by similitude theory. After that the scaling laws are derived. Finally, a numerical simulation and relative error analysis are given to demonstrate the scaling laws.

Residual Flux Density Measurement Method of Single-Phase Transformer Core Based on Time Constant

Residual flux density in the single-phase transformer core can dramatically increase inrush current when the transformer is energized. To reduce inrush current, it is necessary to study residual flux density measurement. This paper proposes a new residual flux density measurement method based on time constant. Firstly, the generation principle of residual flux density is analyzed under different magnetization states, and it is found that the positive relative differential permeability is smaller than the negative at different residual flux density. To obtain the relative differential permeability, when an appropriate DC excitation is applied, the measurement circuit is equivalent to a first-order RL circuit. Then, combining magnetic circuit and transient circuit analysis, the relationship between time constant and relative differential permeability is obtained. It is conclusion that the positive time constant is less than the negative. Residual flux density direction is determined by comparing the positive and negative time constant, and the magnitude of residual flux density is calculated by the relationship between residual flux density and the difference of the positive and negative time constant. Finally, the empirical formula between residual flux density and time constant difference of the square core is obtained in finite element method, and then verified on the experimental platform. Compared with other measurement methods, the relative error of proposed empirical formula is within 4.58 %, and it has higher accuracy in this paper. The proposed method in this paper can provide a reference for selecting the demagnetization voltage, which improves the effectiveness of demagnetization.

DC Fault Analysis Models of Three Converter Topologies Considering Control Effects

Existing converter models are normally reduced as simplified electrical components, whereas it overlooks the impacts of fast dynamics of converter current control loops. Therefore, the dc fault current calculation with the traditional simplified converter models becomes invalid when the simulation time is longer. To overcome this problem, this article incorporates the control effects of converters during the transient process and proposes three dc fault analysis models of classical three converter topologies for the high-voltage dc (HVdc) application including line communicated converter (LCC), two-level voltage-source converter (VSC), and modular multilevel converter (MMC). For an LCC-based rectifier, the nonlinear part of original model is first linearized with the least square method due to the large dc-link voltage deviation during dc fault, and the proportional integral (PI) current regulator with the reduced linearized model can be equivalent as an RC circuit for dc fault analysis. However, for two-level VSC or MMC, the dc-link voltage deviation does not drop that much with a large dc-link capacitor discharging process during transient dynamics. As a result, the original model is linearized relying on the small-signal method based on prefault operation points, and the dynamics of fast inner current loop with the linearized model can be represented as an RL circuit for dc fault current calculation. for dc fault analysis The proposed dc fault analysis models of three converters as equivalent RLC circuits are well testified under different fault resistances and dc reactors, control parameters, and operating conditions. Moreover, dc fault simulations of a hybrid HVdc system have verified the effectiveness of the proposed converter models.

Optimization and modelling methodologies for electro-viscoelastic sandwich design for noise reduction

In this paper a multilayered laminated sandwich with viscoelastic core, surface bonded piezoelectric patches and shunted damping is optimized in order to reduce sound radiation. The viscoelastic core is used since it is especially effective in damping higher frequencies while the piezoelectric patches can actuate on the lower end by tuning its circuit accordingly. Firstly, a single objective optimization is conducted to obtain the optimal stacking parameters of the laminate. Secondly, a multi-objective optimization approach is developed to distribute the piezoelectric shunted patches on the top of the sandwich panel, where the objectives are to reduce the weight, the sound radiation, and the number of shunted RL circuits. The sound radiation characteristics of different configurations are assessed by calculating their radiated sound power through the Rayleigh integral. Finite element analyses are conducted with the use of commercial software ANSYS© and the optimization procedures are implemented with the use of MATLAB© functions.

Non-Differentiable Function Tracking

The tracking problem of desired signal can be transformed to an equivalent stabilization problem about the origin in the error co-ordinate provided the desired signal is differentiable. If the desired signal is not differentiable, then it is not straightforward to solve the tracking problem. In this brief, a methodology based on fractional operators has been suggested to solve this tracking problem, for those classes of non-differentiable reference signals which are integrable. The simulation results of its application to a switch controlled RL circuit is demonstrated.

Integrated computational intelligent paradigm for nonlinear electric circuit models using neural networks, genetic algorithms and sequential quadratic programming

In this paper, a novel application of biologically inspired computing paradigm is presented for solving initial value problem (IVP) of electric circuits based on nonlinear RL model by exploiting the competency of accurate modeling with feed forward artificial neural network (FF-ANN), global search efficacy of genetic algorithms (GA) and rapid local search with sequential quadratic programming (SQP). The fitness function for IVP of associated nonlinear RL circuit is developed by exploiting the approximation theory in mean squared error sense using an approximate FF-ANN model. Training of the networks is conducted by integrated computational heuristic based on GA-aided with SQP, i.e., GA-SQP. The designed methodology is evaluated to variants of nonlinear RL systems based on both AC and DC excitations for number of scenarios with different voltages, resistances and inductance parameters. The comparative studies of the proposed results with Adam’s numerical solutions in terms of various performance measures verify the accuracy of the scheme. Results of statistics based on Monte-Carlo simulations validate the accuracy, convergence, stability and robustness of the designed scheme for solving problem in nonlinear circuit theory.

On flow of electric current in RL circuit using Hilfer type composite fractional derivative

This paper deals with an interdisciplinary research work between Mathematical sciences and Electrical engineering to develop fractional model of Resistance-Inductance circuit (RL circuit). Authors obtained the analytical solution of this fractional model in terms of Mittag-Leffler function. Graphical interpretation of solution also discussed in this paper.

Damping of piezoelectric space instruments: application to an active optics deformable mirror

This paper presents the shunt damping of a unimorph piezoelectric mirror intended to be used as an active secondary corrector in future space telescopes. We propose to take advantage of the actuation capability of the piezoelectric mirror, to increase its natural damping during the critical launch phase of the spacecraft. The piezoelectric actuators, intended to be used for active optics, are shunted on a passive resistive and inductive RL circuit during the launch operation. The proposed concept is verified numerically and experimentally on a piezoelectric deformable mirror prototype, developed on behalf of the European Space Agency. We show that the shunt damping significantly reduces the response of the most critical mode of the mirror (− 23 dB) as well as the stress in the mirror when subjected to a typical vibro-acoustic launch load. This reduces the risk of damaging the mirror during the delicate launch phase, without increasing the complexity of the design.

An Accurate and Efficient Approach for High‐Frequency Transformer Parameter Extraction

Accurate parasitic parameter extraction of high-frequency transformers is one of the key techniques to efficiently design a Switched-mode power supply(SMPS). An approach to accurately and efficiently extract the parasitic parameters of high-frequency transformers is proposed. The high-frequency transformer is first decomposed into first-order RL and second-order RLC circuits according to inherent step response characteristics. Through the measured discharging pulse and damped oscillation responses of the high-frequency transformer excited by a square wave, we can extract the equivalent circuit parameters through fitting the responses with Particle swarm optimization(PSO). The equivalent circuits of the high-frequency transformer with the desired parameters are obtained for the SMPS design. We validate the effectiveness and accuracy of the proposed method with simulations and measurements.

Modeling and Analysis of Inductive “Kickback” in Low Voltage Circuits

Contribution: A didactic methodology, based on analytical expressions and experimental validation, to describe the process of abrupt current interruption in a series RL circuit, that considers real passive components and uses a toggle switch as disconnecting device. Background: In undergraduate courses, circuits adopted in transient analysis usually assume electrical switches in their ideal form, disregarding electrical impedance and its variation over time. Texts and instructors rarely point out these simplifications, so students can become confused. There is thus a need for a suitable switch model that yields a behavior consistent with real devices, while permitting a mathematical formulation of the inductor current. Intended Outcomes: That students should understand electrical component modeling, and how models can represent the physical phenomena that occur in electrical circuits. Application Design: An experiment, designed to evaluate students’ perceptions of switch modeling, modeled a switch by using three different equivalent circuits of increasing complexity, to allow a more realistic simulation. Electrical switch modeling is described, with the models being based on measurements performed on a real circuit. Findings: Student performance was evaluated qualitatively through test scores, and quantitatively through a post-class questionnaire. The results indicate that 96.15% of the students were able to propose an accurate model of the electrical switch.

A Method for Optimally Designing Snubber Circuits for Buck Converter Circuits to Damp LC Resonance

A method for optimally designing RL and RC snubber circuits is presented to reduce the electromagnetic interference caused by parasitic LC resonance. The Q factor of the resonance is used as the design criteria. Optimum snubber parameters are determined analytically and uniquely by using a simplified equivalent circuit of the resonant loop and deriving an analytical formula for the Q factor as a function of the snubber parameters. The optimally designed snubbers can adequately adjust the Q factor to any design target. They can also minimize the increases in the negative effects of the snubbers, i.e., overshoot and power loss. The method was applied to RL and RC snubbers to be added to a synchronous buck converter. The effects of the snubbers were reproduced by simulation program with integrated circuit emphasis (SPICE) simulation to validate the method from the perspective of resonance damping, overshoot, and power loss. The results showed that the damping effects obtained with the optimized snubbers met the Q factor design targets. They also demonstrate that the parameters are optimum in terms of suppressing overshoot and power loss. These results indicate that the method is suitable for optimizing RL and RC snubbers to damp parasitic LC resonance.