Equivalent Circuit Parameters Research Articles

Исследование характеристик литий-ионной аккумуляторной батареи

Purpose: To conduct research on obtaining data, that ties lithium-ion battery voltage to perturbing effects of current flow, to synthesize accumulator equivalent circuit, to obtain algorithm for calculating element parameters for accumulator equivalent circuit on experimental data basis with subsequent check of the model adequacy. Methods: Prognosing battery work that doesn’t correspond to real one at accumulator equivalent circuit synthesis. Equivalent-circuit models of cells plays a battery state though they do not possess all characteristics of physical model. Results: Algorithm for lithium-ion battery equivalent circuit synthesis has been considered, physical experiment on finding accumulator equivalent circuit parameters was conducted, mathematical model on the research results has been compiled and its adequacy has been confirmed. Practical significance: The pursued study made it possible to work out algorithm for calculating parameters to form the algorithm of lithium-ion battery functional diagnosis.

The Induction Motor MRAS-Based Speed Estimator Capable of Modelling the Slip Frequency Dependent Variability of the Rotor Impedance

Speed feedback is indispensable not only for closed-loop controlled induction motors (IM) but also for the state monitoring systems of open-loop controlled IMs. Replacing speed sensors with speed estimations has many advantages including, e.g., hardware complexity reduction, sensor cabling elimination, and reduction of IM drive costs. From the various methods for IM speed estimation proposed in the literature, the model reference adaptive system (MRAS)-based speed estimator stands out because of its straightforward synthesis technique and lower computational complexity. On the other hand, this estimator is inherently sensitive to mismatching of IM equivalent circuit parameters. During transients, when the slip frequency cannot be temporarily controlled over the assumed operating point, rotor impedance varies with the slip frequency changes. This phenomenon is even more significant for open-loop controlled high-slip IMs (NEMA design D IMs), which operate under the cycling load like in, e.g., oil well pumps. The rate and the range of rotor impedance variability are related to the rate and the range of the slip frequency changes. Therefore, a speed estimator capable of modelling the slip frequency dependent variability of the rotor impedance may be required, particularly for the state monitoring systems of open-loop controlled IMs. This paper presents an MRAS-based speed estimator developed on the IM space vector model with the rotor impedance variability modelled by the parallel connected branches of the series rotor equivalent resistance and leakage inductance. The experimental test results confirm the precise speed estimation of the tested IMs achieved by the devised MRAS-based speed estimator in the considered slip frequency range and indicate its potential industrial application.

Estimation of the Equivalent Circuit Parameters in Transformers Using Evolutionary Algorithms

The conventional methods of parameter estimation in transformers, such as the open-circuit and short-circuit tests, are not always available, especially when the transformer is already in operation and its disconnection is impossible. Therefore, alternative (non-interruptive) methods of parameter estimation have become of great importance. In this work, no-interruption, transformer equivalent circuit parameter estimation is presented using the following metaheuristic optimization methods: the genetic algorithm (GA), particle swarm optimization (PSO) and the gravitational search algorithm (GSA). These algorithms provide a maximum average error of 12%, which is twice as better as results found in the literature for estimation of the equivalent circuit parameters in transformers at a frequency of 50 Hz. This demonstrates that the proposed GA, PSO and GSA metaheuristic optimization methods can be applied to estimate the equivalent circuit parameters of single-phase distribution and power transformers with a reasonable degree of accuracy.

Evaluation of a physically defined silicon quantum dot for design of matching circuit for RF reflectometry charge sensing

This paper reports on the extraction of the equivalent circuit model parameters of a physically defined silicon quantum dot at a cryogenic temperature and design of the impedance matching circuits to improve the performance of a charge sensor for radio-frequency (RF) reflectometry. The I-V characteristics and the S-parameters of the quantum dot device are measured around a Coulomb peak at 4.2 K. The measured results are modeled by an RC parallel circuit, and the model parameters for the quantum dot device were obtained. We consider three impedance matching circuits for RF reflectometry of a quantum dot: shunt capacitor-series inductor type, shunt inductor-series capacitor type, and shunt inductor-series inductor-type. We formulate and compare the sensitivity and bandwidth of RF reflectometry for the three types of circuits. The analysis should be useful for selecting the optimal matching circuit and the circuit parameters for given equivalent circuit parameters and working frequency. This procedure is demonstrated for a quantum dot with the characterized model circuit along with simulated performance. This design technique of matching circuit for RF reflectometry can be applied to any device that can be represented by an RC parallel circuit. These results will facilitate to realize fast semiconductor qubit readout in various quantum dot platforms.

Impulse Response-Based Induction Machine Model for Starting Simulation Considering Deep-Bar Effect

This paper proposes a novel model for the starting simulation of induction machines (IMs) where its dynamics are computed directly from the impulse response produced by finite element analysis (FEA). This model realizes an accurate starting simulation owing to considering the skin effect of the cage rotor winding, which cannot be entirely represented by the conventional equivalent circuit model even if several auxiliary branches are added on its rotor side to reduce the modeling error in the high-frequency region. Furthermore, the dynamics can be computed by simply executing the convolution integral for the impulse response and input voltage. In other words, the model requires no fitting or approximation to determine the equivalent circuit parameters, which has been studied extensively in many kinds of literature. For the starting characteristics as an example, the accuracy of simulations using the model was investigated thorough comparing its result with that of measurement and FEA. These researches demonstrated that the proposed model provided a remarkable improvement for the starting simulation.

Эквивалентирование участков электроэнергетических систем на основе режимных параметров в узлах эквивалентирования

When modeling steady-state and transient operating modes in electric power systems, it is necessary to determine a section of the electrical network to simplify the processes occurring in the area not covered by equivalenting. In this case, it is necessary to identify equivalents and relationships with respect to the speci-fied section. The purpose of the research is to determine the parameters of the equivalent sections of power systems and their relationships with respect to the given nodes. Methods of mathematical modeling of the elements of power systems, methods of the theory of electric circuits, and methods of matrix analysis are used. To verify the results, electrical circuits of existing power systems and the software package “Auto-mated Workplace of Relay Protection and Automation Service” have been applied. The implementation of the algorithm is carried out using programming in the Python environment. An algorithm to determine the parameters of equivalent circuits of positive, negative and zero sequences is developed and tested when solving the problem of equivalenting a network section with respect to given nodes. Comparison of the levels of currents in case of short circuits according to the developed algorithm and the software package “Automated Workplace of Relay Protection and Automation Service” in the equivalent nodes shows the high accuracy of the equivalent results in accordance with the developed algorithm. The algorithm considers transformer connections when equivalenting with respect to the nodes located at different voltage classes, as well as phase shifts caused by the star-delta conversion.

Negative Group Delay Metamaterials Based on Split-Ring Resonators and Their Application

In this report, negative group delay (NGD) metamaterials based on split-ring resonators (SRRs) are discussed. A theoretical analysis is proposed to calculate the equivalent circuit parameters, NGD values, and S21 amplitudes of two types of SRRs. Metamaterials made from tantalum nitride are simulated, and the parameters of the two types of SRRs are discussed. Prototypes of metamaterials were fabricated and tested. Measured real-world results were found to be consistent with theoretical and simulated predictions. For EC-SRR, a negative group delay of up to −0.1 ns was achieved at 12–13 GHz. For SR-SRR of the same size as the out ring of EC-SRR, a negative group delay of up to −0.04 ns was achieved, with a loss lower than 2.7 dB. The proposed SRRs were applied to continuous transverse stub (CTS) antenna to reduce the beam walk. The simulation shows that the beam walk can be reduced using the proposed metamaterial.

An equivalent modeling method of passive components with multi‐resonant frequency

SummaryHigh‐frequency characteristics of passive components are crucial to the electromagnetic compatibility (EMC) of an electronic system, and modeling of passive components is of significance for EMC analysis. However, challenges remain in the modeling of passive components with multiple resonant frequencies. In this paper, a method for establishing equivalent models of multi‐resonant frequency passive components, including capacitors, inductors, and resistors, is proposed. Firstly, high‐frequency equivalent circuit topologies of the multi‐resonant frequency passive components, which are simple, easy to understand, and can be applied to the modeling of passive components with various impedance characteristics, are developed. Secondly, a calculation method of equivalent circuit parameters based on least squares and particle swarm optimization (PSO) is presented, which is not sensitive to the initial value, only needs the estimated range of the equivalent circuit parameters, and very suitable for getting the parameters of equivalent circuit models accurately and efficiently. Finally, to validate the method, some SPICE models of single components are established, and a PCB‐level EMC analysis is implemented. The comparisons of the simulated and experimental results show the validity and accuracy of the method. The method is very useful for future components modeling when doing EMC design or other high‐frequency designs.

Parameter Identification of Asynchronous Load Nodes

Asynchronous loads (AL), because of their low negative-sequence resistance, produce the effect of reduced unbalance at their connection points. Therefore, proper modeling of unbalanced load flows in power supply systems requires properly accounting for AL. Adequate models of the induction motor can be realized in the phase frame of reference. The effective use of such models is possible only if accurate data on the parameters of induction motor equivalent circuits for positive and negative sequences are available. Our analysis shows that the techniques used to determine these parameters on the basis of reference data can yield markedly disparate results. It is possible to overcome this difficulty by applying parameter identification methods that use the phase frame of reference. The paper proposes a technique for parameter identification of models of individual induction motors and asynchronous load nodes. The results of computer-aided simulation allow us to conclude that by using parameter identification, we can obtain an equivalent model of an asynchronous load node, and such a model provides high accuracy for both balanced and unbalanced load flow analysis. By varying load flow parameters, we demonstrate that the model proves valid over a wide range of their values. We have proposed a technique for the identification of asynchronous load nodes with such asynchronous loads, including electrical drives equipped with static frequency converters. With the aid of the AL identification models proposed in this paper, it is possible to solve the following practical tasks of management of electric power systems: increasing the accuracy of modeling their operating conditions; making informed decisions when taking measures to reduce unbalance in power grids while accounting for the balancing adjustment effect of AL.

A novel 24 GHz circularly polarised metasurface rectenna

AbstractA novel 24 GHz circularly polarised metasurface rectenna for wireless power transmission is designed in this study. Based on experimental measurements and retro‐simulation, an effective approach is proposed to extract the parasitic parameters of a Schottky diode. A highly efficient millimetre wave rectifier with a measured efficiency of 63% is constructed based on the exact equivalent circuit parameters of a diode. A circularly polarised metasurface antenna is adopted as the receiving antenna, and the gain is enhanced by introducing metal vias around the metasurface. The antenna and the rectifier are connected directly via a microstrip line. Measurements show that the metasurface antenna has a gain of 11.3 dBic and an axial ratio of 2.5 dB at 24 GHz. The measured conversion efficiency of the rectenna reaches 63% at 300 Ω load when the input power is 15.2 dBm. The rectenna has the advantages of low profile, which can be conformal to the electrical equipment.

A CVT Parameter Identification Method Based on Improved Grey Wolf Optimizer

Aiming at the problem that harmonic simulation model parameters of capacitive voltage transformer (CVT) are difficult to determine, an identification method of equivalent circuit parameters of CVT is proposed. By studying the frequency response, a nonlinear equation about the equivalent circuit parameters of CVT is established. By analyzing the characteristics of the equation and combining with the actual use, an improved grey wolf optimizer is applied to achieve the accurate identification of the key parameters of CVT. On the basis of grey wolf optimizer, the algorithm introduced a good point set and comprehensive dimension learning strategy to prevent the algorithm from falling into local optimum, and modified the convergence factor according to the actual needs to improve the convergence accuracy. Finally, three numerical examples are simulated by MATLAB/Simulink software, which proves the feasibility and superiority of the proposed method in CVT application.

A New Varactor-Tuned 5.8 GHz Dielectric Resonator Band-Stop Filter for ITS and C-V2X Coexistence with Vehicular DSRC

In this paper, we introduce an electronically tuneable band-stop filter based on a dielectric resonator, along with its design principles and equivalent circuit model aimed at the coexistence of intelligent transport systems (ITS) and cellular vehicle-to-everything (C-V2X) communications operating at 5.9 GHz, with the widely spread vehicular dedicated short range communications (DSRC) at 5.8 GHz. The proposed architecture involves a dielectric resonator coupled via a microstrip transmission line to a planar ring resonator. The resonance is electronically tuned by varying the bias voltage of a varactor diode placed in the ring. This design is analyzed theoretically and experimentally. For validation, a filter operating at 5.8 GHz was designed. The prototype is capable of enhancing coexistence exhibiting to features. First, when inserted into the ITS transmitter chain, it reduces unwanted transmitter emissions in the out-of-band spectrum occupied by the DSRC carriers in the 5.8 GHz frequency band of at least 25 dB, with a minimal insertion loss at 5. 9 GHz of 1.6 dB; secondly, when inserted in the ITS receiver chain, it exhibits high linearity that prevents the generation of intermodulation products falling into the filter pass band. The prototype features more than 21 dBm of third-order input intercept points, and a tuning range of 26 MHz while maintaining a minimal loaded Q factor of 93. The prototype is discussed regarding the detailed equivalent circuit parameter extraction and their dependency upon the control voltage.

Optimization of the operating mode of a squirrel-cage induction motor

THE PURPOSE. The presented work aims to optimize the operating mode of an asynchronous motor (AM) with a short-circuited rotor. To implement energy-efficient modes of operation of AM, operating in the resources of a rational electric drive, it is necessary to determine the numerical values of the parameters of the AM equivalent circuit, the currents flowing through the circuit element. There is no significance to this important definition of squirrel-cage currents, in accordance with the identification of the allocation of squirrel-cage rotor currents, which requires a solution along with the determination of the parameters of the IM equivalent circuit.METHODS. To analyze the work of AM in technical and educational formulations, equivalent circuits are presented, which turn into circuits with serial and analytical connections of active and inductive connections. For the established and transient operating modes of AM, it is important to determine the stator and rotor currents, their active and reactive components. In this regard, it is proposed to present the IM equivalent circuit in the form of conductivities connected in parallel, which will allow determining the components of IM currents without complex mathematical models. The replacement circuit of AM consisting of a series and parallel connection of active and inductive resistances has been converted into a circuit consisting of conductances. When converting the AM equivalent circuit, no additional dependencies and coefficients were introduced, and all assumptions that are accepted for IM equivalent circuits refer to the circuit under consideration. RESULTS. It was decided to use the equivalent circuit of one phase of AM, expressed in terms of the conductivities of the stator and rotor. According to the found dependences of conductivities, for the proposed equivalent circuit, the corresponding currents and powers of the AM phase are determined. Formulate the basic principle of optimal frequency control of AM, according to the criterion of energy saving. As an indicator of the efficiency of AM operation in steady-state operating modes, the minimum value of the total losses of the engine, the value of which is determined by the ratio of the product of the active conductivity of the rotor circuit q2s and the active conductivity of the phase q to the square of total conductivity y.CONCLUSION. Based on the results of the analysis of the characteristics of an asynchronous motor, the following conclusion was drawn: the motor will operate with minimal losses if the amplitude of the supply voltage is changed so that the slip of the asynchronous motor is equal to the critical value sξ for a given frequency. For the investigated engine AIR100S4, the critical value is sξ=0.0613 at a network frequency of 50 Hz. The method proposed in the work allows to reduce the loss of active power by 3-5% in the motor windings.

Bilayer Lipid Membrane as Memcapacitance: Capacitance-Voltage Pinched Hysteresis and Negative Insertion Conductance.

Inelastic (dissipative) effects of different natures in lipid bilayer membranes can lead to hysteresis phenomena. Early, it was shown that lipid bilayer membranes, under the action of a periodic sinusoidal voltage, demonstrate pinched-hysteresis loops in the experimental capacitance-voltage dependences and are almost the only example of the physical implementation of memcapacitance. Here, we propose an equivalent circuit and mathematical framework for analyzing the dynamic nonlinear current response of a lipid bilayer membrane as an externally controlled memcapacitance. Solving a nonlinear differential equation for the equivalent circuit of a membrane in the form of a parallel connection of a nonlinear viscoelastic capacitor and an active resistance using the small parameter method, we obtain explicit analytical dependences for the current response of the membrane and pinched-hysteresis loops. The explicit solutions and their comparison with experimental data allow us to identify the lumped equivalent circuit parameters that govern the memcapacitor behavior of the membrane and hence the magnitude of the hysteresis. We quantify the memcapacitance hysteresis in terms of negative work done by the control signal. An analysis of the formulas leads to the conclusion that the determining factor for the appearance of pinched hysteresis is the type of nonlinear dependence of the device capacitance on voltage.

Calibrated Electrochemical Impedance Spectroscopy and Time‐Domain Measurements of a 7 kWh Automotive Lithium‐Ion Battery Module with 396 Cylindrical Cells

AbstractA 7 kWh automotive battery module with 396 interconnected cells was tested with electrochemical impedance spectroscopy (EIS) and time‐domain pulsing over 260 charge‐discharge cycles. An EIS calibration workflow was developed for low complex impedance values in a frequency range of 1 kHz to 50 mHz. Significant corrections on the resistance and the reactance were obtained from the calibration, particularly at frequencies above 100 Hz. Equivalent circuit parameters were extracted from the EIS spectra and the pulse response and investigated with respect to the cycle number and state‐of‐charge (SoC). Fit parameters were robustly extracted including Rsol, Rct, and L from EIS, and R0, τ1 and τ2 from time‐domain pulsing. The ohmic resistance decreased over the cycling number indicating an enhanced wetting of the electrodes. Charge transfer resistance Rct showed a monotonic increase over the cycles related to cell ageing. From the charge and discharge pulses, the ohmic resistance R0 was determined from the instantaneous voltage step of the recovery pulse, while the two time constants τ1 and τ2 correspond to the slower exponential recovery phase. R0 from the time‐domain showed a similar trend as Rsol plus a contribution of Rct from EIS. Overall, we show that calibrated EIS and time‐domain pulsing are efficient methods to gain insights into the electrochemical processes related to different SoCs and the cycling ageing of battery modules and packs.

МОДЕЛИРОВАНИЕ АСИНХРОННОГО ЭЛЕКТРОПРИВОДА ДЛЯ ИССЛЕДОВАНИЯ ПРОЦЕССА ПУСКА

A model of an asynchronous motor is proposed, which makes it possible to investigate the process of motor acceleration, taking into account changes in the resistance of the rotor circuit, consumed current and voltage in the power supply network. A method for calculating the parameters of the equivalent circuit of an asynchronous motor according to passport data is proposed, the calculation takes into account changes in the resistance of the rotor circuit during start-up. The electric motor model is based on a static mechanical characteristic with a linear dependence of the rotor resistance on slip. The model is designed to study the electromechanical parameters of the electric drive during the start-up process, taking into account the parameters of the power supply circuit. The analysis of existing functions for modeling the mechanical characteristics of an induction motor was carried out and a formula was chosen for determining the electromagnetic torque from the parameters of a simplified L-shaped equivalent circuit without taking into account electromagnetic transients. Therefore, the proposed model based on the static mechanical characteristic is applicable for mechanisms with a long start. The parameters of the equivalent circuit of an asynchronous motor are determined according to the passport data. The dependence of the rotor circuit resistance on slip is described by a linear function of the first order. The results of calculating the mechanical characteristic according to the compiled model do not differ from the parameters at four known characteristic points corresponding to the passport data of the induction motor. Because when calculating the no-load current and the active resistances of the stator and rotor windings, some assumptions were made, it should be noted that the proposed method is preferable for calculating high-power motors.

The TE201 Waveguide Singlet: A Design Approach Based on Charts

In this work, we analyze the behavior of TE201 waveguide singlets, proposing dimensioning criteria applicable in the portion of the single-mode bandwidth of the input waveguide comprised between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.4f_{c}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.6f_{c}$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{c}$ </tex-math></inline-formula> is the dominant mode cut-off frequency. We address the relationship between the physical features of the singlet and the equivalent circuit parameters, by proposing a method to build ad hoc charts from full-wave simulations based on mode-matching. In the framework of an extracted pole waveguide filter design procedure, the initial dimensioning of the singlets is completed quickly through the charts and the final filter optimization is extremely fast, the initial design being accurate enough. The validation of this procedure is shown with a suitable design example of a filter with zeros both above and below the passband.

НАСТРОЙКА И ИССЛЕДОВАНИЕ РЕЖИМОВ РАБОТЫ НАБЛЮДАТЕЛЯ УГЛОВОЙ ЧАСТОТЫ ВРАЩЕНИЯ РЕГУЛИРУЕМОГО ЭЛЕКТРОПРИВОДА ПОСТОЯННОГО ТОКА

In modern closed-loop controlled electric drives used in manufacturing, the use of speed, current, torque, and other technological variable sensors is required. In some cases, indirect estimation of the electric drive state vector is required, when the use of technological parameter sensors (primarily speed sensors) is difficult or impossible. One of the problems is the length of the information cable in the feedback channel from the actuator to the power converter, which makes it difficult to use direct measurement methods. There are also difficulties in using sensors in an aggressive environment. For example, in the coal mining industry, electric motors or the entire electric drive are often located in an explosion-proof enclosure, and installing additional sensors will require expensive modernization of the entire system. State observers in sensorless electric drives allow restoring unmeasurable state vector components based on measured electrical signals in the power converters of the electric drive. From the perspective of a closed-loop controlled electric drive system, the main feedback is the feedback on the angular rotation frequency. Electric drives based on separately excited DC motors (SEDC) are simpler to investigate and implement such systems. The linearized mathematical model of an SEDC contains a relatively smaller number of differential equations compared to variable frequency drives due to the presence of independent channels for forming magnetic flux in the air gap and electromagnetic torque, which simplifies the analysis and synthesis of sensorless control systems using speed observers. Researching the observer of angular rotation for DC electric drives allows for developing design skills on a simpler system before moving on to variable frequency drives. Research in this area for both DC and AC electric drives is promising because it allows for an increased range of regulation and accuracy of the output coordinate in sensorless electric drives at the required level. This article is dedicated to the study of the properties of speed observers for DC electric drives with independent excitation of various structures. Aim of research Analysis of rotation frequency observer structure in DC motor drives with error reduction based on the proportional principle. Research methods Theoretical and experimental research methods were used in this study. Theoretical methods included the theory of automatic control, state observer theory, theory of electric drives, theory of electric machines, mathematical modeling, systems of differential equations, Laplace transforms, and numerical methods for solving differential equations. Experimental studies were conducted on a software-hardware complex, where the genetic algorithm method was used to identify the parameters of the electric machine equivalent circuit. Results Analytical expression for the characteristic equation roots for the investigated structure of the DC motor drive's speed observer was obtained. Based on this expression, stability criteria and trends in changes of the quality indicators for the angular velocity estimation were determined with varying observer coefficients.

Моделирование электрических параметров гальванической ячейки в процессе микродугового оксидирования

Microarc oxidation is a promising technology for producing wear-resistant anticorrosive coatings for goods made of valve metals and alloys and is used in many industries. One of the main problems of this technology is low controllability caused by the complexity and interconnectedness of physical and chemical phenomena occurring during the coating process. To solve such problems, digital twins are currently actively used. The paper covers the development of mathematical models that are advisable to use as structural elements of the digital twin of the microarc oxidation process. An equivalent electrical circuit of a galvanic cell of microarc oxidation is given, which takes into account the electrolyte resistance, the part coating resistance in the form of a parallel connection of nonlinear active resistance and capacitive reactance. The authors propose a mathematical model describing the behavior of the equivalent electrical circuit of a galvanic cell of microarc oxidation. A technique for determining the parameters of this model was developed, including the construction of a waveform of changes in the resistance of the cell and its approximation, estimation of the values of resistances and capacitance of the galvanic cell equivalent circuit. The authors proposed a calculation method and developed a Simulink model of the microarc oxidation process, which allows simulating the current and voltage waveforms of a galvanic cell. The analysis of the model showed that the model is stable, controllable and observable, but poorly conditioned, which leads to modelling errors, the maximum value of which is 7 % for voltage and 10 % for current. By the parametric identification method using experimental current and voltage waveforms, the dependences of the parameters of the galvanic cell equivalent circuit on the oxidation time are obtained. It is found that the change in the period average of the galvanic cell active resistance correlates with the coating thickness.

On the construction of stable periodic solutions for the dynamical motion of AC machines

&lt;abstract&gt;&lt;p&gt;This article discusses the stability of periodic responses for the dynamical motion of AC machines from the perspective of Lyapunov function approach. The dynamical motion of AC machines is prototypically modeled as an equivalent linear RLC series circuit with time-variant inductance represented by a linear differential equation with periodic coefficients. Based on the deduced stability conditions, some special identities among the equivalent circuit parameters to ensure the stability of responses and their periodic structures are concluded. Through these conditions, the periodic structure of responses is obtained by using the method of strained parameters. Through a comparison with the experimental results from the specialized practical literatures, a strong agreement with the obtained analytical results is achieved. In addition, from a practical point of views, some future points within the discussion are raised to improve the mathematical modeling of AC machines to obtain a better model and simulation.&lt;/p&gt;&lt;/abstract&gt;