Nonlinear Electrical Circuit Research Articles

Proposal of Quantitative Analysis Method for Non-linear Electric Circuits Composed of Light Bulbs

Proposal of Quantitative Analysis Method for Non-linear Electric Circuits Composed of Light Bulbs

Study of subharmonic oscillation processes in ferroresonance circuits

The article presents a general theory of the analysis of subharmonic oscillations at a frequency of 25 Hz in three-phase Ferro resonance circuits with common magnetic conductors. The abbreviated equations are obtained by averaging with the corresponding phases. From the condition of the existence of a periodic solution, the phase and amplitude ratios of the excited oscillations are determined, which differ from threephase circuits with a separate ferromagnetic element. In steady-state mode, the excitation conditions and the area of existence are determined depending on the parameters of the circuit, the bias current and the applied action. The stability of the solution of the initial system of nonlinear second-order differential equations is also studied by analysing the roots of the characteristic equation using a qualitative method. In the theory of nonlinear electrical circuits, the analysis of the physical processes occurring in threephase Ferro resonance circuits during the excitation of second-order subharmonic oscillations is of particular importance in the design and creation of various converter devices.

Structure optimization design and magneto-mechanical characteristics analysis of amorphous alloy with oriented silicon steel composite wound core

Three-dimensional wound cores are widely used in three-phase distribution transformer due to the symmetrical magnetic circuit structure. Amorphous alloy and oriented silicon steel are two kinds of ferromagnetic materials commonly used to make distribution transformer cores, each has own advantages and disadvantages in magnetic and mechanical characteristics. The amorphous alloy and oriented silicon steel composite core can synthesize the advantages of both. In this paper, a double-layer composite wound core (DCWC) structure is proposed and the corresponding dual nonlinear electric circuit and magnetic circuit coupling model is established. A structure optimization design method for the DCWC based on the free parameter scanning method is proposed by taking the percentage of oriented silicon steel in the composite core and the structure parameters as free variables. Based on the proposed optimization design method, a DCWC is designed and the experimental prototypes are manufactured. Further, the flux density distribution, core loss and mechanical vibration displacement of the DCWC are analyzed, and the effectiveness of the proposed method is verified by comparing with the measured results.

Stabilization of highly nonlinear stochastic coupled systems with Markovian switching under discrete-time state observations control

This paper investigates the stabilization of highly nonlinear stochastic coupled systems (HNSCSs) with Markovian switching under discrete-time state observations control. Different from most existing literature, the condition in which the diffusion coefficient and drift coefficient fulfill the linear growth condition is removed. In other words, the coupled systems considered are highly nonlinear. Combining the graph theory and Lyapunov method, we establish the stability criteria for HNSCSs with Markovian switching. Meanwhile, the upper bounded for duration between two successive state observations is proposed. Furthermore, the theoretical results are applied to study the stability of nonlinear electric RLC circuits. Lastly, a numerical example with simulations is provided to show the viability of obtained results.

Features of the Relaxation Process in an RC Circuit under the Influence of a Sinusoidal Voltage

The article is devoted to the study of the properties of the relaxation process in a nonlinear electrical circuit under the sinusoidal voltage influence. Electronic devices and processes the operation of which is based on relaxation principles are sources of specific series of pulses, the monitoring of which allows one to draw conclusions about the technical parameters of these devices and processes. The occurrence of a series of partial discharges in a high-voltage device can serve as an example. An essential factor of partial discharges is their multiplicity both in time and in space, which are dispersed in an a priori unknown number of defects. The aim is to determine the number of defects and to perform appropriate grouping of the entire set of partial discharges by defects. Internal deterministic correlations derived as a result of solving the problem and presented in terms of the classical theory of electrical circuits should be regarded as a key to solving the problem that was set forth. Analytical correlations for the deterministic component of partial discharges in potential electrical insulation defects are revealed. The obtained correlations characterize the time intervals between individual discharges inside the insulation defect. These time intervals are uniquely related to the defect parameters and can serve as a basis for identifying this defect against the background of other partial discharges. As an example, the result of mathematically modeling a relaxation process with the specified parameters is given.

Signal and Power Integrity IO Buffer Modeling Under Separate Power and Ground Supply Voltage Variation of the Input and Output Stages

This work presents an improved input–output (IO) buffer model for signal and power integrity simulation, including power/ground supply voltage (PGSV) variations for the buffer’s input and output stages. Both stages are mathematically modeled from a formulation that is derived from nonlinear electrical circuit analysis, an important aspect that grants these models a good level of generality and, simultaneously, high accuracy. The proposed IO buffer model is linear in the parameters and, therefore, extractable through the linear least-squares technique from the signals acquired in an IO buffer characterization setup. Several validation scenarios, supported on two CMOS driver’s transistor technologies, are performed to evaluate the accuracy of the proposed model. In addition, a comparative analysis is provided, confronting the proposed model’s performance against that of the input/output buffer information specification (IBIS) model, evidencing an outstanding modeling improvement provided by the proposed model.

Long-term potentiation mechanism of biological postsynaptic activity in neuro-inspired halide perovskite memristors

Perovskite memristors have emerged as leading contenders in brain-inspired neuromorphic electronics. Although these devices have been shown to accurately reproduce synaptic dynamics, they pose challenges for in-depth understanding of the underlying nonlinear phenomena. Potentiation effects on the electrical conductance of memristive devices have attracted increasing attention from the emerging neuromorphic community, demanding adequate interpretation. Here, we propose a detailed interpretation of the temporal dynamics of potentiation based on nonlinear electrical circuits that can be validated by impedance spectroscopy. The fundamental observation is that the current in a capacitor decreases with time; conversely, for an inductor, it increases with time. There is no electromagnetic effect in a halide perovskite memristor, but ionic-electronic coupling creates a chemical inductor effect that lies behind the potentiation property. Therefore, we show that beyond negative transients, the accumulation of mobile ions and the eventual penetration into the charge-transport layers constitute a bioelectrical memory feature that is the key to long-term synaptic enhancement. A quantitative dynamical electrical model formed by nonlinear differential equations explains the memory-based ionic effects to inductive phenomena associated with the slow and delayed currents, invisible during the ‘off mode’ of the presynaptic spike-based stimuli. Our work opens a new pathway for the rational development of material mimesis of neural communications across synapses, particularly the learning and memory functions in the human brain, through a Hodgkin–Huxley-style biophysical model.

Investigation of synchronization for coupled quantum nonlinear electrical LC circuits with mutual inductance

Investigation of synchronization for coupled quantum nonlinear electrical LC circuits with mutual inductance

On the controllability and observability of fractional proportional linear systems

This paper deals with generalised Caputo fractional proportional linear time-invariant systems in a finite-dimensional space. The Laplace transformation method ensures the analytical solution of the desired fractional linear time-invariant systems. The present article presents the necessary and sufficient conditions for controllability and observability of the generalised Caputo proportional fractional linear time-invariant systems. These two properties can play a more fundamental role in system analysis before controller and observer designs are engaged. Moreover, we have acquired the criterion for generalised Caputo proportional fractional linear time-invariant systems as Kalman rank conditions. Some numerical examples are presented to show the applicability of the paper to demonstrate our findings. Finally, we derive the necessary and sufficient controllability conditions for the generalised Caputo proportional fractional-order nonlinear Chua's electric circuit.

A data-driven nonlinear frequency response approach based on the Loewner framework: preliminary analysis

We propose a hybrid method based on the combination of computed-aided nonlinear frequency response analysis with the Loewner framework, for the characterization of nonlinear dynamical processes with application in electrochemistry. The method is data-driven, i.e., requiring only samples of the first two generalized transfer functions of the underlying system, given as values of the sampled nonlinear frequency response. Then, the established system fitting and complexity reduction approach (in the frequency domain), known as the Loewner framework, is used to extract the system's invariant quantities. In this analysis, we have used a nonlinear electrical circuit model as a test case, for which the new method provides good results.

Analysis of subharmonic oscillations in three-phase Ferroresonant circuits with bias

In the theory of nonlinear electrical circuits, the analysis of physical processes occurring in three-phase Ferroresonant circuits during excitation of subharmonic oscillations (SHO) of the second order is of particular importance in the design and creation of various converter devices. From the point of view of creating multi-phase secondary power sources (phase-discrete devices, frequency dividers, switching elements, automation and relay protection devices, etc.), the study of second-order SHO excitation in three-phase Ferro resonant circuits with bias is of greatest interest. The article deals with the excitation of second-order subharmonic oscillations in three-phase self-oscillatory circuits with common magnetic circuits with a bias winding. Shortened equations are derived using the averaging method with appropriate phases. From the condition for the existence of a periodic solution, the phase and amplitude relationships of the excited oscillations are determined, which are different from three-phase circuits with a separate ferromagnetic element. In the steady state, the conditions of excitation, the region of existence are determined depending on the parameters of the circuit, the bias current and the applied action. The stability of the solution of the original system of nonlinear differential equations of the second order is also studied by analyzing the roots of the characteristic equation by a qualitative method. Numerical realization of the initial considered system of equations described, self-oscillatory processes is given.

Моделирование феррорезонансных режимов в нелинейных электрических цепях с учетом магнитного гистерезиса

Приведено решение задачи численного моделирования феррорезонансных режимов напряжений и токов в электрических цепях, возникающих при последовательном и параллельном соединении нелинейного индуктивного и емкостного элементов. Вебер-амперная характеристика индуктивного элемента задана с учетом гистерезиса. Известно, что феррорезонансные режимы возникают в электрических цепях, содержащих емкостные и нелинейные индуктивные элементы, в том числе силовые трансформаторы, дугогосящие реакторы, измерительные трансформаторы тока и напряжения, электродвигатели. Нелинейность характеристик индуктивных элементов служит причиной того, что при насыщении их магнитных систем происходит изменение дифференциальных индуктивностей, в результате возникают феррорезонансные, часто нештатные и даже аварийные режимы. Для имитационного моделирования магнитного гистерезиса использована модифицированная обратная модель Джайлса-Атертона. Численное интегрирование дифференциальных уравнений, описывающих динамические процессы в электрических цепях, выполнено явным методом Эйлера. Показано, что в результате феррорезонанса возникает тригеррный эффект, проявляющийся в форме скачкообразного изменения состояния цепи, вызванного неоднозначным характером вольт-амперной характеристики для входного напряжения и тока. Предложенный метод моделирования переходных и установившихся режимов в нелинейных электрических цепях с учетом магнитного гистерезиса может быть обобщен на случай произвольных цепей, в том числе, со сложной топологией.

ФЕРРОРЕЗОНАНСНЫЕ ПЕРЕНАПРЯЖЕНИЯ В ЭЛЕКТРОУСТАНОВКАХ 6–220 кВ: ТЕОРИЯ И РЕЗУЛЬТАТЫ ЭКСПЕРИМЕНТАЛЬНЫХ ИССЛЕДОВАНИЙ

Relevance The article is devoted to the systematization and generalization of theoretical and experimental studies of ferroresonance overvoltages in electrical installations 6–220 kV. The need to study this issue is associated with the active introduction of distributed generation facilities into distribution networks, as well as medium and low voltage networks. In power districts with distributed generation facilities, the settings and operation algorithm of relay protection and automation devices differ from the traditional ones used in centralized power supply. The generation parameters and the nature of electromechanical transients also differ, which is caused by the low dynamic stability of generating plants based on synchronous generation and the use of network inverters with energy storage in electronic generation. Thus, due to significant differences in the parameters of the network operation mode with and without distributed generation objects, it is necessary to revise many well-known technical problems, including the issue of ferroresonant processes. Electrical installations of 6–220 kV were chosen as the object of research, since the concept of distributed generation does not imply backbone networks, and the maximum installed power of an individual facility is limited by 25 MW. Aim of Research Aim of research is to systematize and summarize the theoretical and experimental studies of ferroresonance overvoltages in electrical installations 6–220 kV. Research methods To study the circuit-mode conditions for the occurrence of ferroresonant processes in electrical installations of 6–220 kV, an analysis of foreign and domestic publications, standards was carried out, and the theoretical foundations of electrical engineering and the theory of nonlinear electrical circuits were used. Results The physical essence of the phenomenon of ferroresonance, the conditions for the occurrence of ferroresonant processes and measures to prevent them in medium and high voltage networks, experimental studies of ferroresonant processes are considered. The ferroresonant process consists in compensating the inductive and capacitive resistances in the oscillatory circuit with a saturated inductance core. There are various modes of ferroresonance, which are determined by the initial conditions: fundamental, subharmonic, aperiodic and chaotic. A prerequisite for the occurrence of a ferroresonant process is the power of the power source sufficient to saturate the inductance core. Non-linear inductance that can participate in the formation of an oscillatory circuit are voltage transformers, power transformers, shunt reactors. The capacity of the circuit can be a power line, a busbar system, a capacitor bank, shunt capacitors of switches. Hardware and operational measures to protect against ferroresonant processes in electrical installations are aimed at changing the capacitance or inductance of network elements that may participate in the formation of a ferroresonant oscillatory circuit, preventing the formation of such a circuit or reducing its quality factor. The results of experimental studies of ferroresonant processes do not contradict the guidelines for protection against resonant voltage increases in electrical installations. Keywords: ferroresonance overvoltages, distributed generation, ferroresonant process, electrical installation, busbar system, high-voltage switch, non-linear inductance

Treatment of Nonlinear Electrical Circuits by the Caputo-Fabrizio Derivative

Treatment of Nonlinear Electrical Circuits by the Caputo-Fabrizio Derivative

ФЕРРОРЕЗОНАНСНЫЕ ПРОЦЕССЫ В СИСТЕМАХ ЭЛЕКТРОСНАБЖЕНИЯ С РАСПРЕДЕЛЕННОЙ ГЕНЕРАЦИЕЙ

Relevance The article is devoted to the study of the possibility of occurrence of ferroresonant processes in power supply systems with distributed generation. Ferroresonant processes cause overvoltages in electrical installations and lead to their failure. In backbone and distribution networks without distributed generation facilities, the phenomenon of ferroresonance has been studied quite deeply, effective hardware and operational measures have been developed to prevent the occurrence of ferroresonance surges in electrical installations. However, the issue of the occurrence of ferroresonant processes in power supply systems with distributed generation, which is a promising direction in the development of the energy sector, seems to be little studied. Aim of research The main aim of the research is to investigate circuit-mode conditions for the occurrence of ferroresonant processes in power supply systems with distributed generation. Research methods To study the circuit-mode conditions for the occurrence of ferroresonant processes in power supply systems with distributed generation, the main provisions of the theory of electrical complexes and systems, the theory of nonlinear electrical circuits, and the principles of controlling objects of electrical complexes and industrial systems were used. Results The circuit-mode conditions for the occurrence of ferroresonant processes in power supply systems with distributed generation are studied. The power supply system of a HF radio center, containing a power plant with a lower installed power or corresponding to the maximum power consumption of the load, was chosen as the object of study. The features of the scheme-mode conditions for the occurrence of ferroresonant processes under conditions of distributed generation are as follows. Due to the insignificant remoteness of distributed generation facilities and consumers, additional opportunities arise for subharmonic ferroresonant processes. When a generating plant is connected to low-voltage busbars, conditions are created for the occurrence of a ferroresonant process involving low-voltage windings of power transformers. The low dynamic stability of generating installations of distributed generation facilities based on synchronous generators reduces the likelihood and duration of ferroresonant processes in the event of phase wire breaks and short circuits on the power line. Generating plants connected via grid inverters have a limited output current and can be turned off by emergency automatics in the event of an emergency operation of the grid, which, as a rule, precedes the appearance of ferroresonant overvoltages in electrical installations. Thus, in power districts with distributed generation facilities, the circuit-mode conditions for the occurrence of ferroresonant processes, known in the centralized power supply system, undergo changes, and it is also possible to form new ferroresonant oscillatory circuits. Keywords: distributed generation, ferroresonant process, power supply system, oscillatory circuit, generating plant, relay protection and automation devices Acknoledgements: The work was carried out under the state order of the Omsk Scientific Center of the Siberian Branch of the Russian Academy of Sciences (project state registration number 122011200349-3).

Construction of exotical soliton-like for a fractional nonlinear electrical circuit equation using differential-difference Jacobi elliptic functions sub-equation method

The deal of this paper is to use the differential-difference Jacobi elliptic functions sub-equation method for constructing exact solutions of nonlinear electrical circuit including intrinsic fractional-order in the sense of Riemann–Liouville derivatives. According to the algorithm of a unified symbolic computation, we attain several solitons solutions as solitary waves train, singular kink-type soliton, doubly periodic solitons, grey and anti-grey soliton-like. These findings are emerged and constructed by means of the three Jacobi elliptic functions. These types of functions provide hyperbolic, trigonometric, exotic and doubly periodic fractional exact solutions which have not yet been reported in the studied model. For this studied model, The new solutions obtained are exotic soliton-like that have not been observed yet. And they provide new propagative’s modes through the cn, dn, sn Jacobi elliptic functions for the fractional nonlinear electrical pass band circuit. Therefore, further investigations on differential-difference Jacobi elliptic functions sub-equation method should help researchers to discover more soliton solutions for other nonlinear discrete systems.

The quantum dynamics of a mesoscopic driven RLC circuit consisting of a linear inductor, a linear resistor and a nonlinear capacitor

The nonlinear capacitor that obeys of a cubic polynomial voltage–charge relation (usually a power series in charge) is introduced. The quantum theory for a mesoscopic electric circuit with charge discreteness is investigated, and the Hamiltonian of a quantum mesoscopic electrical circuit comprised by a linear inductor, a linear resistor and a nonlinear capacitor under the influence of a time-dependent external source is expressed. Using the numerical solution approaches, a good analytic approximate solution for the quantum cubic Duffing equation is found. Based on this, the persistent current is obtained antically. The energy spectrum of such nonlinear electrical circuit has been found. The dependency of the persistent current and spectral property equations to linear and nonlinear parameters is discussed by the numerical simulations method, and the quantum dynamical behavior of these parameters is studied.

Dynamics and wave propagation in nonlinear piezoelectric metastructures

This paper reports dynamical effects in one-dimensional locally resonant piezoelectric metastructures leveraged by nonlinear electrical attachments featuring either combined quadratic and quartic, or essentially quartic potentials. The nonlinear electromechanical unit cell is built upon a linear host oscillator coupled to a nonlinear electrical circuit via piezoelectricity. Semi-analytical harmonic balance (HB)-based dispersion relations are derived to predict the location and edges of the nonlinear attenuation band. Numerical responses show that weakly and moderately nonlinear piezoelectric metastructures (NPMSs) promote a class of nonlinear attenuation band where a bandgap and a wave supratransmission band coexist, while also imparting nonlinear attenuation at the resonances around the underlying linear bandgap. Besides, strongly nonlinear regimes are shown to elicit broadband chaotic attenuation. Negative capacitance (NC)-based essentially cubic piezoelectric attachments are found to expand the aforementioned effects over a broader bandwidth. Excellent agreement is found between the predictions of the HB-based dispersion relations and the nonlinear transmissibility functions of undamped and weakly damped NPMSs at weakly and moderately nonlinear regimes, even in the presence of NC circuits. This research is expected to pave the way toward fully tunable smart periodic metastructures for vibration control via nonlinear piezoelectric attachments.

An equivalent electrical circuit for the Hindmarsh‐Rose model

SummaryHardware realizations of neural networks can pave the way towards a new generation of processors due to the biological role model being superior in terms of speed and energy‐efficiency compared to today's processors. This can be achieved by deriving novel design principles for circuits being obtainable when replicating and investigating real biological neural networks in depth. This has, for example, been done by utilizing the Hindmarsh‐Rose model, offering a rich repertoire of neuronal firing patterns. Our aim is to synthesize a theoretical, equivalent electrical circuit of the Hindmarsh‐Rose model being well interpretable in terms of biology, since this supports the derivation of design principles from biology and can serve as a basis for a systematic circuit simplification. We do this by starting from a linearized model because this allows for a systematic approach and then first derive a linear and afterwards a nonlinear equivalent electrical circuit. The resulting circuit has a structure similar to conductance‐based models, where a deployed negative impedance converter can be seen as a deeper modeling of ion pump activity. Simulation results of the proposed circuits show the functionality of the equivalent circuits.

ПІДВИЩЕННЯ ЕФЕКТИВНОСТІ ДІАГНОСТИКИ ШИХТОВАНИХ ОСЕРДЬ ТА ВИЗНАЧЕННЯ ПОТОЧНОГО СТАНУ СИНХРОННИХ ДВИГУНІВ

Topicality. Today a large number of synchronous motors with long mean-time-between-failures operate under the conditions of industrial enterprises. They are mainly characterized by difference from the published electromagnetic parameters and degraded energy and reliability indicators, increased heating of the windings and electromagnetic vibrations, which causes a reduction in power on the shaft. Among other reasons, this is due to changes in the properties of laminated stator cores, which is the main structural element that is not replaced during repairs. Purpose. Determination of the main set of independent diagnostic parameters that would reliably distinguish the main types of defects of stator cores, first of all loosening and shorting, during their local testing using induction method and features of artificial neural networks in problems of video identification of core surface and determination of the state of synchronous motors. Metodology. The research methods of theoretical calculations of nonlinear electric circuits with non-sinusoidal power supply and methods of video identification for determination of diagnostic parameters and defects of laminated cores and the theory of neural networks in determining the current state of cores and synchronous motors in general were used during the research. Results. The obtained results specify the conditions of local testing of laminated cores from the standpoint of determining the required set of diagnostic parameters sensitive to the main types of defects, using a contactless test method, reveal the features of the use of neural network analyzers to determine the defects of the tooth zone by video identification and substantiate the principles of application of artificial neural networks in problems of predicting the states of major structural units and synchronous motors in general, due to changing properties of stator cores. Originality. The obtained results allow determining the state of the stator core and taking into account the influence of its change on the current state of synchronous motors with long or intensive operation. Practical value. The research results make it possible to assess the changes in the main parameters and characteristics of synchronous motors, determined by the actual state of the laminated stator cores and take into account their impact on energy efficiency, reliability and other operating parameters of synchronous motors. References 10, figures 7.