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This paper aims to evaluate the possibilities of fractional calculus application in electrical circuits and magnetic field theories.

The analysis of mathematical notation is used for physical phenomena description. The analysis aims to challenge or prove the correctness of applied notation.

Fractional calculus is sometimes applied correctly and sometimes erroneously in electrical engineering.

This paper provides guidelines regarding correct application of fractional calculus in description of electrical circuits’ phenomena. It can also inspire researchers to find new applications for fractional calculus in the future.

This paper seeks to give an outline about the geometric concept of electronic circuits, where the jump behavior of nonlinear circuits is emphasized.

A sketch of circuit theory in a differential geometric setting is given.

It is shown that the structure of circuit theory can be given in a much better way than by means of a description of circuits using concrete coordinates. Furthermore, the formulation of a concrete jump condition is given.

In this paper, an outline is given about the state of the art of nonlinear circuits from a differential geometric point of view. Moreover, differential geometric methods were applied to two example circuits (flip flop and multivibrator) and numerical results were achieved.

This work is intended to historically commemorate the one hundredth anniversary of the invention of a new type of electronic circuit, referred to in 1919 by Abraham and Bloch as a multivibrator and by Eccles and Jordan as a trigger relay (later known as a flip-flop).

The author also considers the circuit-technical side of this new type of circuit, considering the technological change as well as the mathematical concepts developed in the context of the analysis of the circuit.

The multivibrator resulted in a “circuit shape” which became one of the most applied nonlinear circuits in electronics. It is shown that at the beginning the multivibrator as well as the flip-flop circuits were used because their interesting properties in the frequency domain.

Therefore, it is a very interesting subject to consider the history of the multivibrator as electronic circuits in different technologies including tube, transistors and integrated circuits as well as the mathematical theory based on the concept from electrical circuit theory.

The main purpose of this paper is to estimate the resistance and inductor in the RL electrical circuit when these are unavailable or missing data that it is a concern in electrical engineering. The input voltage is assumed to be corrupted by the noise and the current is observed at discrete time points.

The authors propose a computationally efficient framework for parameters estimation using least square estimator and Bayesian Monte Carlo scheme.

The explicit formulas for least square estimator are derived and the strong consistency of resistance estimator is verified when inductor is a known parameter, then Bayesian estimation of parameters governed by using Markov chain Monte Carlo methods. The applicability of the results is demonstrated by using numerical examples. Several numerical results and figures are presented via Matlab and R programming to illustrate the performance of the estimators.

The paper can be used in various types of electrical engineering real time projects. The projects include electrical circuits, electrical machines theory and drives, especially when the parameters are uncertain that it is a worry in electrical engineering.

To the author's best knowledge, least square and Bayesian estimation of resistance and inductor have not been studied before. The proposed model is nonlinear with respect to inductor (L); therefore the present work has fundamental difference in comparison with the similar models.

The purpose of this paper is to make a study of electromagnetic interference between electrical power lines and nearby underground metallic pipelines.

The equivalent electrical circuit of the studied electromagnetic interference problem between electrical power lines and nearby metallic pipelines is created and solved using a loop currents technique based on a hybrid method. The used circuit solving technique was implemented in a software application developed by the authors.

The authors have identified the influence of phase sequence on induced voltage level in an underground pipeline for a double circuit electrical power line. Also the effect of different normal operation and phase to earth fault currents have been revealed.

The study has been made through a research project with the Romanian gas transportation company, in order to find the proper protection techniques for underground metallic pipelines.

The paper reveals the influence of some electrical and geometrical parameters that have not been studied in detail previously.

The purpose of this paper is to identify on the instantaneous electrical power basis of a nonsinusoidal periodic current three-phase asymmetric system, active and reactive positive, negative and zero sequence powers, taking into account higher harmonics. The main power theories, including those embodied in the IEEE 1459 standard, do not allow to evaluate some of power components.

A well-known fact is that the three-phase AC system total power with the symmetry of currents and voltages is constant. It corresponds to the electrical energy transfer process in a DC system. In this case, the electrical energy transmission can be taken as high quality. It has been established that the components of active and reactive powers are because of the product of current and voltage of unidirectional sequences. The orthogonal components of the oscillating power are because of the product of the voltage and current components of different sequences, with the exception of the zero sequence.

For an unbalanced nonsinusoidal mode of a three-phase system, the components of instantaneous power were defined, corresponding to the active and reactive positive and negative and zero sequences powers with the selection of the fundamental and higher harmonics. The active and reactive powers of sequences were divided into two categories – consumed and generated.

It is proposed to use the ratio of “interfere” power RMS value to the total power RMS value to assess the instantaneous power distortion.

The purpose of this paper is to simulate micro direct methanol fuel cells (DMFCs) for portable electronic devices by means of a non‐linear equivalent circuit based on a fully coupled, dynamic, electrochemical model.

The equivalent circuit accounts for electrochemical reactions and electric current generation inside the catalyst layers, electronic and protonic conduction, fuel crossover across the membrane, mass transport of reactants inside the diffusion layers. The V‐I characteristic of the device is obtained by combining mass transport and electric equations. The transient dynamics is accounted for by an equivalent capacitance, while the slow dynamics by the mass conservation equation. The equivalent circuit is embedded in the Matlab/Simulink^® dynamic model of a hybrid system, consisting of a micro fuel cell and a Li‐ion rechargeable battery.

An original equivalent circuit of a passive DMFC suitable for static and dynamic simulations under variable loading conditions is proposed and validated.

The one‐dimensional model of the micro cell does not take into account transverse mass transfer and current density variations in the cell layers, which can be due to non‐homogeneous materials or to the complex dynamics of the convective mass flow in the reservoir and in the room air.

The equivalent circuit can be used for simulating the dynamic performance in realistic operating conditions when the fuel cell is used to supply the electronic equipment through a power management unit.

The DMFC is described from an electrical point of view as a controlled non‐linear generator; such equivalent representation is particularly suited for designing power management units for electronic portable devices.

The paper presents two new algorithms of controlled switching the power transformer. The purpose of this paper is to obtain formulas that determine the moments of closing of the circuit breaker poles. The study contains projects of control systems for both algorithms.

Mathematical formulas for the time instants of the breaker poles closing were developed on the basis of electric circuit theory and magnetic circuit theory. The presented systems were simulated using a model created in the Alternative Transients Program/Electromagnetic Transients Program software.

Numerical simulations have proved that the shown systems properly perform the controlled switching carried out in accordance with the proposed algorithms. The times of the poles closing were correctly determined and the inrush currents were reduced to a level of the current of unloaded transformer.

The results achieved are better than those shown in the literature. The solutions presented in the literature provide a reduction of inrush current to a value comparable to the rated current of the transformer, which is ten times greater than the no-load current. Additional achievement of the work is the development of analytical formulas that determine the times of the breaker poles closing.

The purpose of this paper is to introduce an efficient model for analysis of the voltage distribution along the long ceramic insulator strings in a high‐voltage tower window, especially when the structure and parameters of the ceramic insulator are unknown. The effect of the grading ring on the voltage distribution is also investigated.

A circuit model composed of capacitors is used to analyze the voltage distribution along the ceramic insulator strings in a transmission tower window. The capacitances of the disk insulators, line conductors, and tower are obtained by using the finite element method, charge simulation method, boundary element method, and measurement according to their characteristics.

The model is very efficient. The voltage distribution along insulator strings can be optimized by adjusting the parameters of the grading ring. The maximum amount of voltage applied to a single insulator disk can be reduced effectively by increasing either the diameter of the grading ring or the distance from the upper surface of the grading ring to the high‐voltage end of the insulator string.

The model is very efficient for analysis of the voltage distribution along the long ceramic insulator strings, especially when the structure and parameters of the ceramic insulator are unknown.

The purpose of this paper is to model multilayer structure surface acoustic wave (SAW) sensors, incorporated in CMOS or micro‐electro‐mechanical system integrated circuits, and to derive the corresponding wave velocity as an analytic expression in terms of the layers‘ thickness and density, which is suitable for analysis and design.

The method is based on an electro‐mechanical equivalent model of multilayer structure SAW sensors. A multilayered SAW device is represented by a two‐port electrical equivalent circuit consisting of three parts: input transducer, output transducer, and between them the delay line, which is the sensing part. The sensing part is modelled as a mechanical two‐port network. The wave velocity is calculated using analogy between the mechanical and electrical quantities and the fact that the wave motion of the SAW extends below the surface to a depth of about one wavelength.

The presented model predicts very efficiently and accurately the velocity of SAW sensors with multilayer substrates in the case where the thicknesses of upper layers are much smaller than the signal wavelength. The velocity can be calculated from the formula, so that elaborate numerical computations involving partial differential equations are avoided.

The model and the velocity calculation can be applied only to acoustically thin upper and middle layers where acoustically thin means that a layer is sufficiently thin and rigid (large shear modulus). The presented results provide a starting‐point for further research in the analysis and design of sensors fabricated using AlGaN, GaN, AlN/diamond.

Since the majority of SAW sensors is designed with acoustically thin layers, the proposed model and calculation can be of interest for many practical material combinations. The presented model and calculation can be used in most cases of the optimal sensor design with respect to the sensor sensitivity or required area on the sensor chip.

The paper presents a new original model of multilayer structure SAW sensors and a new method of SAW velocity calculation. The method gives good results, with much simpler calculations than in the wave equation method, in cases where certain layers are acoustically thin.