Current Components Research Articles

SPEED CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTOR IN SLIDING MODE

The paper examines a series of speed control algorithms for a synchronous permanent magnet motor in sliding mode, providing asymptotic stability of the first, second, and third order. In the sliding mode, the control system exhibits properties that are unattainable with classical continuous control algorithms. The control algorithms are developed based on the inverse dynamics method combined with the minimization of local instantaneous energy functionals. The key idea of the method lies in the reversibility of the direct Lyapunov method for stability analysis. The closed-loop control system has a predefined Lyapunov function, represented by the instantaneous energy. Notably, the control algorithms do not require knowledge of the object's parameters or differentiation operations, which facilitates their practical implementation. The regulator parameters consist solely of coefficients used to specify the desired duration and shape of current and motor speed transient processes. The vector speed control system comprises two controllers for the stator current components and the motor speed controller. All regulators operate in sliding mode. The output signals of the stator current component controllers and speed vary discontinuously from maximum to minimum values. Simulation results demonstrate the effectiveness and high-quality performance of the control algorithms. To determine the control performance indicators for the three synthesized speed controllers, the motor startup trajectory is formed from characteristic segments of constant, linearly increasing, and parabolic signals. The speed control algorithm with a first-order asymptote ensures zero tracking error only for a constant reference signal. With a linearly increasing reference signal, the steady-state relative tracking error is 2,5 %, while for a parabolic reference signal, the error varies between zero and 2,5 %. The second-order asymptotic speed control algorithm ensures zero steady-state tracking error for constant and linearly increasing reference signals, and for a parabolic reference signal, the steady-state relative tracking error is 0,125 %. The third-order asymptotic speed control algorithm ensures zero steady-state tracking error for constant, linearly increasing, and parabolic reference signals, with a maximum dynamic relative tracking error of 0,05 %.

Increasing the Energy Efficiency of Traction Electric Drives of Direct Current

Purpose. The work is aimed at improving the energy efficiency of direct current traction electric drives of electric transport by introducing transistor pulse width converters (PWC) with an optimal switching frequency to minimize total electrical losses in the electric drive. The electrical losses of traction electric drives consist of electrical losses in the armature winding and in the PWC transistors. Methodology. To study the dependence on the switching frequency of transistors, the electrical losses in the armature winding and PWC transistors are divided into two parts: static losses from the direct current component of the current and dynamic losses, i.e., losses in the armature winding from harmonic current components and losses in the transistors from transient switching currents. Since the dynamic electrical losses in transistors increase with increasing frequency and decrease in the armature winding, it is necessary to find the optimal PWC co-mutation frequency at which the total dynamic losses in the traction electric drive will be minimal. The goal of increasing energy efficiency in a traction electric drive is achieved by determining the dependence of dynamic electrical losses in the armature winding on the switching frequency of the PWC and computer modeling of the transistor electric drive. Findings. It is found that the relative dynamic electrical losses in the armature winding in the case of polyharmonic power supply are equal to the square of the armature current ripple coefficient. An algorithm for determining the optimal switching frequency of the PWC is developed: 1) the dependence of dynamic electrical losses on the switching frequency of transistors is determined experimentally on computer models of the motor and PWC; 2) the graph of the dependence of total dynamic electrical losses of the transistor electric drive on the time-tothe point of minimum losses, which corresponds to the optimal frequency value, is determined. Originality. For the first time, the authors obtained an analytical expression for the relative dynamic electrical losses in the armature windings, which are equal to the square of the armature current ripple factor. Practical value. Establishing the optimal switching frequency of the PWC according to the developed methodology reduces electrical losses in traction electric drives, i.e., increases their energy efficiency.

A characterization of soft-error sensitivity in data-parallel and model-parallel distributed deep learning

The latest advances in artificial intelligence deep learning models are unprecedented. A wide spectrum of application areas is now thriving thanks to available massive training datasets and gigantic complex neural network models. Those two characteristics demand outstanding computing power that only advanced computing platforms can provide. Therefore, distributed deep learning has become a necessity in capitalizing on the potential of cutting-edge artificial intelligence. Two basic schemes have emerged in distributed learning. First, the data-parallel approach, which aims at dividing the training dataset into multiple computing nodes. Second, the model-parallel approach, which splits layers of a model into several computing nodes. Each scheme has its upsides and downsides, particularly when running on large machines that are susceptible to soft errors. Those errors occur as a consequence of several factors involved in the manufacturing process of current electronic components of supercomputers. On many occasions, those errors are expressed as bit flips that do not cause the whole system to crash, but generate wrong numerical results in computations. To study the effect of soft error on different approaches for distributed learning, we leverage checkpoint alteration, a technique that injects bit flips on checkpoint files. It allows researchers to understand the effect of soft errors on applications that produce checkpoint files in HDF5 format. This paper uses the popular deep learning PyTorch tool on two distributed-learning platforms: one for data-parallel training and one for model-parallel training. We use well-known deep learning models with popular training datasets to provide a picture of how soft errors challenge the training phase of a deep learning model.

Multi-source data driven harmonic spectrum estimation of substation feeder current

With the proliferation of non-linear loads and distributed power resources that connect through power electronic equipment, decentralized harmonic pollution in three-phase symmetric power system becomes increasingly serious. Despite this, monitoring the current harmonic of all substation feeders regardless of cost is unrealistic. To this end, a multi-source data driven method is proposed in this paper, utilizing data from the power quality monitoring system, dispatching system, and market business system, to estimate the harmonic spectrum of substation feeder currents and estimate the harmonic current components of each feeder with monitoring data of bus voltage harmonics and line harmonic currents. The objective function of the harmonic spectrum estimation model is constructed based on the analysis of current harmonic phasor and power relationship on the feeders. An improved particle swarm optimization (PSO) algorithm is proposed to solve the proposed estimation model thereby obtaining the current harmonic content of each feeder and the phase angle difference between the current harmonics of the feeders. The performance of the proposed model and algorithm is validated by numerical simulation with a test system and an actual system.

50 YEARS FIELD ORIENTED CONTROL OF THREE-PHASE AC DRIVES IN THE PRACTICE - THE STATE OF THE ART

From DC motors (DCM) we know, it is possible to independently control the two currents of the flux and torque generating. Because the two DCM circuits are completely isolated, we obtain simple adjustment algorithms that require little computing time on the microprocessor. For this reason, DCM has been at the forefront of the application of digital controls in drive control systems in the early years, especially in high-performance systems. On the contrary, the three-phase AC motor (ACM) has a complex structure due to the winding system and three-phase power supply, and has caused significant difficulties in the mathematical description of the above decoupling characteristics. The purpose of the field-oriented control (FOC) is therefore to create a tool that allows the decoupling control of the flux and torque-producing current components from the three-phase AC currents flowing in the coil. The FOC drive system is a system based on the principle of decoupling the above power components thanks to the stator current feedback control (the innermost circuit of the drive system). The FOC-type control method belongs to the class of vector control methods for electrical machines. On the occasion of the 50th anniversary of FOC, this paper aims to provide an overview of the development status of FOC in industrial practice. The content presented deals mainly with 3-phase induction motors.

Application of Amorphous and Nanocrystalline Soft Magnetic Materials in Balanced-Force-Type Electromagnetic Relay.

The magnetic properties of soft magnetic materials, including their saturation magnetic induction strength and permeability, significantly affect the dynamic characteristics of electromagnetic relays. However, the soft materials most commonly used for relays in the magnetic conductive components of electromagnetic systems, such as electrical pure iron, limit further relay design improvement and optimization to a certain extent. Thus, this paper proposes the use of amorphous and nanocrystalline soft magnetic materials with good high-frequency magnetic properties in magnetic circuits. A wavelet analysis was conducted on the high-frequency components of the coil current while the relay operated, and the corresponding magnetic materials were selected. Considering the challenges in processing amorphous and nanocrystalline materials and collecting test data for the accuracy verification of simulation methods, we prepared a scaled-up prototype for use in dynamic characteristic tests. The simulation method was improved, yielding more accurate simulation results regarding the relay's dynamic characteristics. On this basis, six replacement schemes using amorphous and nanocrystalline materials were considered. The test results proved that this application could improve the relay's dynamic characteristics. Finally, a full-size sample with an iron core consisting of nanocrystalline alloy 1K107B was prepared, and the conclusions were verified in tests.

Methodology for determining the degree of magnetic induction of transformers with a sinusoidal magnetic flux

The research presented in the article is aimed at reducing losses in the magnetic circuits of electrical machines. These losses amount to up to 5 % of the generated electricity, do not depend on the load and can increase over the life of the equipment. To effectively design and construct transformers with low no-load losses, total losses in steel are minimized by optimizing the crystal grain size and thickness of core sheets, improving the steel texture and magnetic circuit design, etc. However, the hysteresis, classical eddy current and anomalous eddy current components of losses in steel react in different directions to these measures, which does not effectively minimize total losses. To determine the three components of losses, a modernized method of three frequencies is proposed, which takes into account the dependence of the hysteresis loss coefficient on frequency. A formula for correcting this coefficient is derived. It is shown that the indicator of the degree of magnetic induction given in most modern scientific sources in the expression for eddy current anomalous losses has become irrelevant. A method for calculating this indicator for the core of a specific transformer is presented, which uses the loss components and total losses in steel found by the method of three frequencies and the total losses in steel at a reduced primary voltage. For the transformer under study, the degree of magnetic induction in anomalous losses was 1.88. The results obtained can be used in the design of dry and oil transformers of different powers operating with a sinusoidal magnetic flux.

A Simulation Study of the Modulation of the Geomagnetic Field Configuration on the Seasonal Variation of Ionospheric Sq Currents

AbstractBased on Global Coupled Ionosphere‐Thermosphere‐Electrodynamics Model, the solution of the 3‐dimensional current in the ionospheric region, the equivalent sheet current and filed‐aligned current are examined. The simulation study enables a comprehensive analysis of the effect of the geomagnetic field configuration, especially the non‐dipole component and tilt angle, on the ionospheric electrodynamics phenomena. Different geomagnetic field configurations are specified in the present work, including realistic geomagnetic field (RGF), tilted dipole geomagnetic field (TDGF) and zero‐declination dipole geomagnetic field (ZDGF). Our simulation focuses on the seasonal variation of Sq current, primarily governed by annual and semi‐annual variation. The modulation of the tilt angle of the geomagnetic field is globally distributed, whereas the modulation of the geomagnetic anomaly is localized. At mid‐latitudes, the annual mean and semi‐annual amplitudes of the Sq current are negatively correlated with the magnetic field strength, especially shown in geomagnetic anomaly area, while there is the opposite effect in the geomagnetic conjugate regions of the opposite hemispheres. The annual variation of Sq current system is more affected by the offset of the geomagnetic latitudes and geographical latitudes. The seasonal variation of the total Sq current is also modulated by the geomagnetic field. The annual mean, the annual and semi‐annual components of the total Sq current are negatively correlated with the magnetic field strength, while the annual variation is also controlled by the tilt angle of the geomagnetic field. The solar radiation affects the semi‐annual variation of the current more strongly than the annual variation.

Analysis of DC bias characteristics of transformer by using fixed-point time-step FEM and dynamic J–A hysteresis model

The injection of the Direct Current (DC) bias component will lead to oversaturation of the transformer core and affect its safe operation. In this paper, the vector magnetic potential A and winding current I are used as the variables solved in the time-step finite element method to simulate the nonlinear transient magnetization characteristics of the transformer under DC bias, and the fixed-point reluctivity is introduced to deal with the nonlinear iterative problem. The field-circuit coupling relationship is established through the electromagnetic induction law, and the two-dimensional time-step finite element model of the transformer core is found. The dynamic J–A hysteresis model is used to deal with the hysteresis effect of iron cores. The fixed-point reluctivity of difference form is introduced to solve the problem of uneven transition and multi-value of magnetization curve with hysteresis in the iterative process. The determination scheme for the equivalent thickness of the core model and the initial iterative value are discussed. A laminated core transformer is made for experiments, and the accuracy and applicability of the model proposed in this paper are verified by comparing the calculation and experimental results. The influence of different voltages and different DC bias components on the electromagnetic characteristics of the transformer is analyzed.

Single-Phase Charging of Six-Phase Integrated On-Board Battery Charger Using Predictive Current Control

Integrated On-Board Battery Chargers (IOBCs) have shown promise as an elegant charging solution for electric vehicles in recent literature. Although the three-phase charging technique of IOBCs has extensively been discussed in the literature, single-phase charging is still a challenging research topic. The Predictive Current Control (PCC) approach has shown many benefits, including a straightforward algorithm, simple implementation, comparatively quick response, and appropriate performance, when compared to conventional control techniques. This paper investigates the impact of single-phase charging of a six-phase-based IOBC system with different winding configurations using PCC, which, up to the best authors’ knowledge, has not been conceived thus far. Under single-phase charging, the zero-sequence current component is utilized to ensure zero torque production during charging mode. Since the impedance of the zero subspace is highly affected by the employed winding design, the performance of PCC with different winding layouts of either induction machine (IM) or permanent magnet synchronous machine (PMSM) is investigated and compared. The proposed method is experimentally validated using a 1.1kW six-phase IM and a 2 kW 12-slot/10-pole PMSM. Finite Element analysis is also carried out to investigate the effect of single-phase charging mode on the induced radial forces and vibration level when PM machine is employed.

The equivalence principle for a plane gravitational wave in torsion-based and non-metricity-based teleparallel equivalents of general relativity

We study the energy–momentum characteristics of the plane “+”-polarized gravitational wave solution of general relativity in the teleparallel equivalent of general relativity (TEGR) and the symmetric teleparallel equivalent of general relativity (STEGR) using the previously constructed Noether currents. The current components describe energy–momentum locally measured by an observer if the displacement vector ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document} is equal to the observer’s 4-velocity. To determine the non-dynamical connection in these theories, we use the unified “turning off” gravity principle. For a constructive analysis of the values of Noether currents and superpotentials in TEGR and STEGR, we use the concept of “gauges”. The gauge changing can affect the Noether current values. We study under what conditions the Noether current for the freely falling observer is zero. When they are established, the zero result can be interpreted as a correspondence to the equivalence principle, and it is a novelty for gravitational waves in the TEGR and STEGR. We highlight two important cases with positive and zero energy, which reproduce the results of previous works with a different approach for determining gravitational energy–momentum in the TEGR, and give their interpretation.

Deep neural networks based method to islanding detection for multi-sources microgrid

One of the significant issues in the field of microgrids is their islanding, where in many cases, the lack of awareness of microgrid islanding can lead to interference in the protective and control functions of the microgrid. Therefore, the accurate detection of microgrid islanding is of utmost importance. In this article, a method based on deep neural networks is presented. The proposed approach utilizes terminal parameters of microgrid resources, such as sequence current components, voltage, and other parameters, to detect islanding. Various operational states of the microgrid are simulated offline as standard test cases, and the parameters of each of them are recorded for later use. These data are then used to extract statistical features using discrete wavelet transform. Subsequently, the extracted features are fed into deep neural networks for training, and the training and evaluation results demonstrate an accuracy of over 99% for the proposed method in terms of precision and reliability. Furthermore, the accuracy of the proposed method is compared with some similar approaches for islanding detection.

Rectifier load modeling and zero voltage switching design of inductive power transfer system with S‐type topology on the secondary side

SummaryRectifier load in inductive power transfer system has nonlinear characteristics. However, the traditional analysis method equates it to a pure resistor, which leads to a certain deviation between the theoretical analysis and the actual circuit. This will reduce the accuracy of the inductive power transfer (IPT) system model and affect the soft switching operation of the inverter. In this paper, the IPT system with S‐type topology on the secondary side is studied. Firstly, the resistance–inductance characteristics of the rectifier load are analyzed by simulation, and then a second‐order circuit response model is established to solve the time‐domain expression of voltage and current. Then, the fundamental component of voltage and current is extracted by Fourier transform to calculate the impedance value of the rectifier load, and the mathematical calculation model of the rectifier load is established. On this basis, the influence of the inductive component of the rectifier load on the input impedance of the IPT system is analyzed. Then, a parameter design method for zero voltage switching is proposed for S‐S and LCC‐S topologies. Finally, an experimental platform of S‐S and LCC‐S IPT system is built. The correctness and effectiveness of the theoretical analysis and the proposed parameter design method are verified by experiments.

Insights into Q-markers of honey-fried licorice in treating spleen deficiency based on substance and energy metabolism regulation

BackgroundHoney-fried Licorice (HFL) is a dosage form of Glycyrrhizae Radix et Rhizome processed with honey, which has been recorded to exhibit better efficacy in tonifying the spleen compared to the raw product. In contrast, different processing methods of Glycyrrhizae Radix et Rhizome exhibit different efficacies and applications, but their current quality control index components remain consistent. PurposeBased on the discovery and research strategy of traditional Chinese medicine decoction piece quality marker (Q-marker), this study aimed to conduct a multidimensional integration of constituents absorbed into the body and metabolomics based on the tonifying spleen and stomach effects of HFL to effectively identify the Q-marker of HFL. MethodsIn this study, a spleen deficiency rat model was established using the "exhausted swimming + poor diet" method to investigate the pharmacodynamics of tonifying the spleen and stomach by HFL. The constituents absorbed into blood was conducted using UPLC-Q-TOF/MS, correlation analysis between metabolomics and constituents absorbed into blood recognized the Q-Marker of HFL. ResultsThe pharmacodynamic data demonstrated that HFL exhibited a significant regulatory effect on the disordered levels of PP, trypsin, chymase, PL, α-Glu, MTL, GAS, VIP, IL-2, IFN-γ, and IgA in the spleen deficiency model. Furthermore, HFL was found to improve the pathological changes in the spleen and intestine in the spleen deficiency model, highlighting its significant "tonifying spleen and stomach" effect. In the serum containing HFL, a total of 17 constituents were identified as being absorbed into the blood. Among these, 11 were prototypical components, while 6 were metabolites. Metabolomics data revealed that 9 differentially expressed metabolic markers were observed. Furthermore, the analysis of endogenous metabolic markers indicated that 10 components exhibited significant correlations with these biomarkers. ConclusionThe effect of "tonifying spleen and stomach" of HFL is closely related to the regulation of the material and energy metabolism pathway. The Q-Marker of HFL is glycyrrhizic acid and 18β-glycyrrhetinic acid as the main control standards and liquiritin, isoliquiritin, liquiritin, isoliquiritin, isolicorice flavonol, licorice chalcone C and Formononetin were used as auxiliary standards.

Power quality enhancement of dual stage three phase grid integrated SPV system using sequential neural network-based algorithm

In this paper, a single-layer sequential neural network (SNN) control algorithm has been proposed for managing the power quality (PQ) in the double-stage three-phase grid-integrated solar photovoltaic (SPV) system. The proposed algorithm efficiently extracts the active and reactive fundamental components of the load current, with a higher convergence rate. The extracted reference currents are matched with the sensed source currents to generate gating pulses for the voltage source converter (VSC). To handle power quality issues in distribution networks such as harmonic imbalances, voltage fluctuations (sags/swells), and the need for active and reactive power compensation, the VSC is controlled very precisely. The control algorithm consists of two-stage processes. In the initial stage, the incremental conductance (INC) based DC-DC converter has been incorporated to extract the peak power from the SPV system. In the later stage SNN-based algorithm is used to control the VSC. A 100 KW solar PV system connected to the utility grid has been designed by using a three-leg VSC in the MATLAB/Simulink environment. The system performance has been evaluated by comparing it to existing techniques. The simulation results comfortably meet the requirements of the IEEE-519–2014 and IEEE 1547–2003 standards for utility grid connection.

Incorporation of multiple random features kernel mean p‐power controller to elevate power quality in reconfigurable grid‐connected residential solar photovoltaic systems

SummaryProblems like intermittent photovoltaic (PV) power, disconnected PV arrays, etc. are brought on by the extensive integration of PV generation. In this article, a single‐stage PV‐integrated grid‐tethered system is controlled using a reconfigurative multiple random features kernel mean p‐power (MRFKMP) control algorithm. The algorithm circumvents the dependence of kernel parameter in the classic random Fourier features mapping and lower the computing complexity in the traditional multiple kernel learning adaptive filter. MRFKMP algorithm with a linear filter structure can reduce both the computational and storage cost. This is the novel application of MRFKMP algorithm to extract fundamental component of nonlinear load currents in PV‐integrated grid‐tied system. Furthermore, to increase the reliability of the system, a reconfigurable control is developed, which adaptive regulates DC link voltage from PV mode (PVM) during PV hours to active power filtering mode (AFM) during PV nonavailability/PV disconnection. On a created laboratory testbed, the applied control's practical feasibility for numerous scenarios is evaluated. Comparison with existing control algorithms reveals that the MRFKMP controller outperforms the LMF based PV system by 79% less peak‐to‐peak load current ripple and 60% less than the best performing SRF control algorithm. The grid current THD is 2.60%, which is 30% low than that presented by SRF technique.

Femoral anterior condyle height decreases as the distal anteroposterior size increases in total knee arthroplasty: A comparative study.

The anterior flange height of the current femoral component increases with an increasing distal femoral anteroposterior dimension. During total knee arthroplasty (TKA), we have observed that a large femur may have a thinner anterior condyle, whereas a small femur may have a thicker anterior condyle. The first purpose of this study was to examine whether the femoral anterior condyle height decreases as the distal femoral anteroposterior size increases and whether gender differences exist in anterior condyle height. A total of 1218 knees undergoing TKA intraoperative and computed tomography scans from 303 healthy knees were used to measure the anterior lateral condylar height (ALCH), anterior medial condylar height (AMCH), and the lateral anteroposterior (LAP) and medial anteroposterior (MAP) dimensions of distal femurs. The LAP and MAP measurements were used for adjustments to determine whether gender differences exist in anterior condyle heights. Linear regression analysis was performed to determine correlations between ALCH and LAP or between AMCH and MAP. There were significant differences between males and females in ALCH in both the CT and TKA groups and AMCH in the CT group (all P<0.01). After adjusting for LAP and MAP, there were significant gender differences in the lateral and medial condylar heights in both groups (P<0.01). There were significant negative correlations between ALCH and LAP values and between AMCH and MAP values in both CT and TKA measurements, with the LAP and MAP values increasing as ALCH and AMCH decreased. The results demonstrate that femoral anterior condylar height decreased with increasing anteroposterior dimension in both the medial and lateral condyle. In addition, this study also showed that anterior condylar heights are highly variable, with gender differences. The data may provide an important reference for designing femoral anterior flange thickness to precisely match the natural anterior condylar anatomy.

Modeling and Simulation of a Planar Permanent Magnet On-Chip Power Inductor

The on-chip integration of a power inductor together with other power converter components of small sizes and high-saturation currents, while maintaining a desired or high inductance value, is here pursued. The use of soft magnetic cores increases inductance density but results in a reduced saturation current. This article presents a 3D physical model and a magnetic circuit model for an integrated on-chip power inductor (OPI) to double the saturation current using permanent magnet (PM) material. A ~50 nH, 7.5 A spiral permanent magnet on-chip power inductor (PMOI) is here designed, and a 3D physical model is then developed and simulated using the ANSYS®/Maxwell® software package (version 2017.1). The 3D physical model simulation results agree with the presented magnetic circuit model, and show that in the example PMOI design, the addition of the PM increases the saturation current of the OPI from 4 A to 7.5 A, while the size and inductance value remain unchanged.

Model Predictive Control of Counter-Rotating Motors for Underwater Vehicles Considering Unbalanced Load Variation

The propulsion system for underwater vehicles, driven by a counter-rotating permanent magnet synchronous motor (CRPMSM), can enhance the operational stability and efficiency of the vehicle. Due to the influence of complex underwater flows, the load imbalance of CRPMSM’s dual counter-rotating rotors may lead to severe issues of dual-rotor desynchronization rotation. Combining traditional vector control (VC) with master-slave control strategies can address the desynchronization problem when CRPMSM’s load changes. However, it results in significant speed fluctuations and a long transition time during the transition from load disturbance to synchronous rotation. This paper introduces a model predictive control (MPC) strategy to effectively resolve this issue. The incremental MPC model is established based on the mathematical model of CRPMSM in the dq coordinate system. The predictive control system forecasts the d- and q-axis components of stator currents for the next four control cycles. It selects the optimal control increments to minimize the cost function based on current predictions and different inverter voltage states. The obtained optimal d- and q-axis components of stator voltage are used to control CRPMSM under unbalanced load disturbances. Simulation results demonstrate that, compared to the VC strategy, CRPMSM utilizing the MPC strategy exhibits better dynamic performance with faster speed response and reduced torque fluctuations during load and speed variations.

Revisiting the Butler-Volmer Electrode Kinetics: Separating the Anodic and Cathodic Current Components of a Quasi-Reversible Electrode Reaction in Staircase Voltammetry

A simple mathematical strategy is proposed to estimate anodic and cathodic current components in voltammetry by combining the basic mathematical model of a quasi-reversible electrode reaction at a conventional planar electrode with the Butler-Volmer electrode kinetics with a goal to simplify and facilitate the measurement of electrode kinetics. In spite of the fact that the separate anodic and cathodic current components are experimentally inaccessible parameters, it is demonstrated for the first time that they can be reliably estimated from the net (total) current over the whole potential interval of a common voltammetry, requiring only the current–potential relationship, without prior knowledge of any electrode kinetic parameter (i.e., the standard rate constant and the electron transfer coefficient). The mathematical procedure requires semi-integration of the current and previous knowledge of the formal potential of the studied redox couple. The theory predicts that very fast electrode processes, with an apparent electrochemical reversible behavior, are associated with anodic and cathodic current components the intensity of which is proportional to the standard rate constant. Thus, the proposed simple methodology provides a new perspective in analyzing voltammetric data and expands the accessible kinetic interval towards very fast electron transfer processes by means of simple voltammetry at macroscopic planar electrodes. The proposed methodology is experimentally illustrated with the electrode reaction of hexacyanoferrate(II) ion oxidation at platinum electrode.