Apparent Inductance Research Articles

An apparent inductance online identification for sensorless control of permanent magnet synchronous motor

AbstractThe model‐based sensorless control of permanent magnet synchronous motor (PMSM) relies on the motor parameters. In practice, the considerable uncertainty of inductance and the difference between the apparent inductance and the incremental inductance exists. To overcome it, an online apparent inductance identification method for PMSM sensorless control is proposed. First, an initial incremental inductance table (IIT) is obtained offline. Then, an asymmetric high‐frequency square wave injection method is proposed to identify the incremental inductance at the operation point, and an adaptive minimum adjustment algorithm is proposed to adjust IIT automatically. Finally, the apparent inductance is calculated using the adjusted IIT. Based on it, the complete PMSM sensorless control is designed. The experimental results indicate this method is feasible and effective.

Modeling HTS non-insulated coils: A comparison between finite-element and distributed network models

High-temperature superconducting (HTS) non-insulated (NI) coils have the unique capability to bypass current through conductive turn-to-turn contacts, mitigating the possibility of a catastrophic failure in the event of a quench. However, this turn-to-turn conductivity leads to a significant increase in the coil decay/charging time constant. To understand this phenomenon, several modeling techniques have been proposed, including the lumped and distributed network (DN) circuit models, and more recently the finite-element (FE) models. In this paper, the decay results obtained from modeling HTS NI pancake coils using both a DN model and a 2D FE model approach are evaluated and compared. Steady-state fields, and transient charging and decay behaviors are calculated with each model and the results compared. Key differences are highlighted, including the computation speed and the capturing of various physical phenomena. Both models exhibit non-exponential decay during initial coil discharge due to current redistribution between the inner and outer turns. In addition, the FE model exhibits other effects arising from current redistribution in both the radial and axial directions, including remanent magnetization, and variation of the “apparent total inductance” during charging. Simulations of sudden discharge have also been analyzed using the common “lumped circuit” formula. This shows that extracted values for the apparent surface contact resistance between coil windings can differ by more than a factor of 5 from the initial input value. Our results confirms the optimal choice of architecture for future NI coil models and emphasize that caution should be exercised when interpreting experimental results using the lumped circuit approach.

Parameterization of the apparent chemical inductance of metal halide perovskite solar cells exhibiting constant-phase-element behavior

A better characterization of the rich variety of anomalous ionic-electronic mechanisms in organic-inorganic metal halide perovskite solar cells is essential to obtain a stable and physically robust interpretation of the dynamic responses obtained. Therefore, new approaches towards light intensity-induced effects understanding are intensively searched for. Among all the mechanisms whose elucidation is locked and still under live debate, the apparent inductance phenomena stand out, which are visible not only in photovoltaic devices and optoelectronic elements, but also, for instance, in electrochemical and biological systems. Usually, the negative loops in impedance spectra are modeled through ideal elements (negative capacitance or inductance) although the results show systematic deviations (constant-phase-element behavior). In most scenarios, the influence of chemical inductance dispersion is somehow neglected, that is, ideal conditions are mimicked, omitting the practical device operation. Here we reformulate the theory that captures the slow (non-electromagnetic) inductive effects in the current-voltage curves of perovskite solar cells, deciphering the microscale behavior, consisting essentially of defects associated with deep trap states, from macroscale observations and experimental measurements. The audience is potentially huge, since many authors of multidisciplinary backgrounds are genuinely interested in adequately interpreting this behavior of general character.

Improved Small-Signal Injection-Based Online Multiparameter Identification Method for IPM Machines Considering Cross-Coupling Magnetic Saturation

A novel online multiparameter identification method is proposed for interior permanent magnet (IPM) machines considering cross-coupling magnetic saturation. The identification method is based on the combination of small-signal impedance model and fundamental frequency signal model under <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -axes. To analyze the nonlinearity of IPM machines, cross-coupling magnetic saturation effect is introduced into online multiparameter identification for the first time. Based on this model, a phase compensation strategy and orthogonal decomposition in phasor domain is proposed to decouple the complicated mathematical model into four linear equations. By injecting voltage small-signals into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -axes, multiparameter of IPM machine including adjusted apparent inductance, incremental self-inductance, incremental mutual-inductance can be identified online in a wide operation region. During this process, no additional computing equipment is required. The proposed method is carried out on a tested IPM machine and verified by the finite-element analysis.

Inductance Analysis of Two-Phase Winding Segmented Permanent Magnet Linear Synchronous Motor

The inductance of a winding segmented permanent magnet linear synchronous motor (WS-PMLSM) is affected by winding disconnection and coupling length variation, which makes the variation of inductance more complicated, and this paper proposes incremental inductance, apparent inductance, and positional inductance to reveal this phenomenon, which gives a theoretical basis for mathematical modeling and thrust fluctuation suppression. First, an analytical approach is used to derive a fully coupled state model using the magnetomotive force and specific permeability function. Second, the domain of the specific permeability function is extended and the inductance expressions are calculated for the whole moving range. Finally, the inductance of the prototype WS-PMLSM with a two-phase winding is experimentally verified, and it is proposed that the effects of the three inductive components on the system should be considered comprehensively when implementing control of the WS-PMLSM.

Effects of DC-Field Excitation on the Incremental Inductance of a Variable Flux Reluctance Machine

This article presents a method for the computation of the incremental inductances in a 12/10 variable flux reluctance machine (VFRM) using the hybrid analytical modeling coupled with a fixed-point nonlinear solver. The variation of incremental and apparent inductance with respect to the dc-field excitation is investigated for both zero and non-zero ac-field excitations. The results show that the difference between both inductance values is not negligible after 25 A/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> dc-current density for the investigated benchmark without the ac field. Moreover, when a non-zero ac field is introduced in addition to the dc-field, the apparent inductance becomes misleading not only under magnetic saturation but also under low excitation in the linear region of the saturation curve. The results obtained with the proposed nonlinear hybrid model are compared with the finite element method in terms of magnetic flux density distribution and incremental inductance value. The root-mean-square discrepancy of magnetic flux density distribution is found to be 37.6 mT. Furthermore, the discrepancy between incremental inductance results of the proposed method and the finite element model is calculated as 1.43%, while the proposed approach requires less post-processing and necessitates ten times less number of degrees-of-freedom.

Current-Controller-Free Self-Commissioning Scheme for Deadbeat Predictive Control in Parametric Uncertain SPMSM

Deadbeat predictive control (DBPC) requires accurate model parameters in its application, therefore it is difficult to use DBPC for surface mounted permanent magnet synchronous motor (SPMSM) with uncertain motor parameters. As a solution, this paper proposes a strategy to obtain the needed parameters, and then uses them to achieve DBPC on SPMSMs whose parameters are unknown. A detailed investigation on parameter sensitivity of DBPC is presented, and attention is paid to different influences between the incremental inductance and the apparent inductance. On this basis, parameter configurations in the DBPC are suggested. And novel current-controller-free self-commissioning schemes are proposed to identify the stator resistance together with the stator inductances under different magnetic saturation levels. Compared with existing commissioning schemes that do not depend on current controllers, solutions for commissioning voltage auto-tuning is provided. So the methods are able to automatically decide the amplitudes of the injected voltage for a given motor, and achieve a controllable current feedback during the commissioning. This brings significant convenience for the inductance identification at a specific saturation level. Moreover, the inverter nonlinearity compensation is not needed but still, identification accuracy can be guaranteed. The feasibility and effectiveness of the proposed method are confirmed by the achieved DBPC and the corresponding current tracking performances on two different SPMSMs.

On-Load Apparent Inductance Derivative of IPMSM: Assessment Method and Torque Estimation

This article presents a new method to evaluate the on-load apparent inductance derivative for interior permanent-magnet synchronous machine (IPMSM) and, consequently, to estimate the on-load reluctance torque. It is well known that the on-load inductances (self and mutual) are dependent of the machine’s electric load, and since the reluctance torque of the IPMSM is the interaction between the armature current and apparent inductance derivatives (self and mutual), the saturation effects in the on-load inductances have a high influence in the reluctance torque (waveform and value), increasing the torque ripple and affecting the machines’ self-sensing capability. If the on-load inductance derivative waveforms are calculated inaccurately or, at least, are affected by numerical errors inherent to the evaluating method, as found when they are assessed by means of differentiating the on-load inductances, which accounts for the high-order harmonic content introduced by the current waveform, the spatial harmonic contribution on the inductance harmonic content, and the non-linearities inherent to the stator and rotor materials, an incorrect on-load reluctance torque is estimated. This way, this article proposes a new numerical method, based on the concept presented in the on-load back electromotive force (EMF) Maxwell stress tensor (MST) method, to properly evaluate the on-load inductance derivatives (self and mutual) in order to avoid and to overcome the drawbacks presented in the differentiating method. The proposed method differs from the back EMF MST based on its own constraints and simulation conditions. On the other hand, it still needs the usage of the frozen permeability method and the Maxwell stress tensor method. The proposed technique is discussed and explained in small details, showing how it overcomes the drawbacks highlighted previously. Finally, the results for two different current waveforms (sinusoidal and non-sinusoidal) are presented in order to validate the proposed method’s accuracy.

Quench Protection Study of the Updated MQXF for the LHC Luminosity Upgrade (HiLumi LHC)

In 2023, the LHC luminosity will be increased, aiming at reaching 3000 fb-1 integrated over ten years. To obtain this target, new Nb3Sn low-β quadrupoles (MQXF) have been designed for the interaction regions. These magnets present a very large aperture (150 mm, to be compared with the 70 mm of the present NbTi quadrupoles) and a very large stored energy density (120 MJ/m3). For these reasons, quench protection is one of the most challenging aspects of the design of these magnets. In fact, protection studies of a previous design showed that the simulated hot spot temperature was very close to the maximum allowed limit of 350 K; this challenge motivated improvements in the current discharge modeling, taking into account the so-called dynamic effects on the apparent magnet inductance. Moreover, quench heaters design has been studied to be going into more details. In this study, a protection study of the updated MQXF is presented, benefiting from the experience gained by studying the previous design. As a result, a study of the voltages between turns in the magnet is also presented during both normal operation and most important failure scenarios.

Inductive Power Transfer System With Self-Calibrated Primary Resonant Frequency

Inductive power transfer (IPT) is a commonly employed technique for wirelessly supplying power to implantable medical devices. A major limit of this approach is the sensitivity of the inductive link to coupling factor variations between transmitting and receiving coils. We propose in this paper a new method for compensating these variations and improving the inductive link efficiency. The proposed technique is based on a mechatronic module that dynamically tunes the primary resonant capacitor value in order to maintain the resonance state of the IPT system. The module is able to maintain resonance state for apparent primary inductance range at least from 0.5 to 5 $\mu {\rm H}$ using a high capacitance resolution of 0.032 pF. Experimentations conducted on a 13.56-MHz IPT system showed a $65\%$ higher power transfer compared to a traditional IPT system.

Linear Model of a Novel 5-Phase Segment Type Switched Reluctance Motor

This paper introduces the general linear magnetic circuit model of a novel 5-phase segment type switched reluctance motor (ST-SRM) of which rotor cores are embedded in an aluminum block as well as to improve the performance characteristics under simultaneous two-phase (bipolar) excitation of windings. The developed model implements the magneto motor force (mmf) that is necessary to produce short and exclusive magnetic flux paths minimizing the commutation switching and eddy current losses in the laminations. For this purpose, an equivalent magnetic circuit for newly developed ST-SRM and the underlying assumptions are given. The concept of apparent inductance and torque equations of two-phase simultaneously excited ST-SRM is introduced and the effectiveness and deficiencies of the linear model are given. DOI: http://dx.doi.org/10.5755/j01.eee.20.1.6159

Microelectromechanical inductors with high inductance density via mechanical energy storage

This paper reports the fabrication, characterization and modeling of microelectromechanical inductor (MEMI) devices, which employ electrodynamic coupling and mechanical energy storage to boost the apparent electrical inductance of electrical conductors. The microfabricated MEMI devices comprise an electrically conducting, mechanically suspended clamped–clamped copper beam that is placed in a transverse static magnetic field. Under an ac current excitation, the beam is forced to vibrate via the electrodynamic interactions between the electrical current and the static magnetic field. This electromechanical coupling results in a large apparent electrical inductance. The microfabrication and subsequent characterization of a variety of test structures is presented. The devices exhibit a peak quality factor up to 5.6 and net areal inductance densities of up to 3.5 µH mm−2. The experimentally observed behavior is compared against theoretical models using extracted system parameters.

Electromechanical devices with enhanced inductance via electrodynamic interactions

This paper presents the concept, theory, and demonstration of electromechanical devices that employ energy conversion and mechanical energy storage in order to boost the apparent one-port electrical inductance. Two different structures – moving-magnet and moving-conductor – are used to demonstrate the concept. An electromechanical lumped element model is derived that both explains the physics and guides the design. Measurements of mesoscale proof-of-concept devices indicate an inductance boost of up to three orders of magnitude compared to static electrical devices, with maximum inductive quality factor up to 7.4. These structures are presented as a first step toward ultra-high-inductance-density microfabricated “electromechanical inductors” ultimately intended for power converter applications.

Large apparent inductance in organic Schottky diodes at low frequency

A large low frequency inductance is found in a Schottky diode composed of regioregular poly(3-hexylthiophene) and aluminum. This apparent inductance is evident in response to both swept frequency sinusoidal, ramp and step voltage inputs above a threshold voltage. The constant slope of the current in response to a voltage step suggests an incredibly large inductance (a few hundred megahenry) in a device that is only 2000μm3 in size. A number of potential mechanisms including chemical reactions, barrier modulation, and memory effects are evaluated in order to find a suitable explanation for the inductive behavior. Similarity in the dc characteristics of the organic Schottky diode and organic bistable devices that are being applied as memory suggests that the current leads the voltage due to increments in tunneling current that occur as charges are gradually stored in localized states.

A Study of Inductance Computations for Transverse Flux Linear Motor Considering Nonlinearity of Magnetic Material

Inductance is an important parameter to assess electric motor characteristics. In this paper, the methods of apparent and incremental inductance calculations are introduced for a transverse flux linear motor (TFLM), which has a peculiar coil shape. To consider the nonlinearity of magnetic material, nonlinear analysis is performed by 3-dimensional equivalent magnetic circuit network (3D EMCN). The calculation method is verified by test results.

Wave speeds for a TLM model of moving media

AbstractIn a companion paper, a transmission line matrix (TLM) scheme was presented for the solution of the 1‐D equation of waves in moving media, ytt+αyxt+βyxx=0, describing the superposition of two waves with direction‐dependent speeds. The TLM model achieved controlled, direction‐dependent wave‐speed bias by means of supplementary link lines with notional ‘diodes’. Expressions for wave speed, presented without proof, were verified. Here a proof is presented using a new, time‐domain approach. The apparent (direction‐dependent) inductance and capacitance as seen by a single wave are first established in a generalized way from the TLM algorithm, from which two wave speeds and impedances are then derived. Copyright © 2002 John Wiley &amp; Sons, Ltd.

A microprocessor-based measuring unit for high-speed distance protection

This paper describes a microprocessor-based measuring unit which is suitable for use in high-speed digital distance relays. The unit uses an algorithm that provides accurate estimates of apparent resistance and inductance of the line in relatively short times. The algorithm deals effectively with the presence of nonfundamental frequency components in signals without making assumptions about their compositions. The hardware and software of the unit are described. Test results indicate that the estimates converge to their true values within about 10 ms after fault inception. Also, the ability of the unit to provide accurate estimates is not adversely affected by the system frequencies drifting from its nominal value and by the distortion of the input signals.

Digital model for transient studies of a three-phase five-legged transformer

A flux linkage model for a three-phase five-legged transformer is derived for the first time. The effects of mutual and leakage inductances, saturation, eddy current loss, hysteresis and residual fluxes of the nonlinear iron core are included. A straightforward and novel method for determining both the apparent and incremental inductance matrices for a loaded two-winding five-legged transformer is derived. Simulations presented in this study are based on apparent inductance (λ/i) rather than incremental inductance (dλ/di) because this approach was found to be preferable for predicting the behaviour of the laboratory transformer used. Eddy current and hysteresis losses are combined into one core loss term which is accounted for by a voltage-dependent resistance load on the secondary. The flux in each segment of the iron core and in the air gaps and tank are computed at each step. The model thus yields a completely detailed description of the transformer&apos;s behaviour. A predictor-corrector algorithm written in FORTRAN is used to solve the set of nonlinear differential equations that describe the transformer. A 386-based computer has been used to generate voltage and current waveforms faithful to laboratory data. Transformer inrush current and ferroresonance are selected as test cases because of the extreme computational demands that these transients place on the computer model. The model can be implemented using only nameplate and conventional test data along with the B-H curve of the core material. The method is thus well suited to the practical needs of engineers in industry.

A 3-D finite element perturbational method for determining saturated values of transformer winding including experimental verification

A method is presented in this paper for the calculation of saturated transformer winding inductances. The method is mainly based on an energy perturbation technique in conjunction with non linear three dimensional finite element vector potential field solutions. The concepts of apparent, effective and incremental inductances were utilized in the methodology presented. The method presented was successfully applied in the calculation of apparent, effective and incremental inductance values of the primary winding of a single phase transformer. Very good agreement between calculated and measured values of inductance was accomplished. The work presented provides methodologies by which one would be able to determine, in conjunction with nonlinear three dimensional field solutions, these values of inductances. These inductance values are very important in the dynamic analysis of electrical devices, steady state calculation as well as energy storage and other related analysis and preformance studies.

Characterization of spiral microstripline inductors

Equations for estimating the true inductance, the apparent inductance and the self-resonant frequency of spiral stripline inductors are presented. Estimates of the unloaded Q and the frequency at which the maximum unloaded Q will appear are found both experimentally and analytically. It is also shown that optimizing the properties of the inductors for a given application is straightforward.