Inductance Matrix Research Articles

Real-Time Detection of Interturn Faults in PM Drives Using Back-EMF Estimation and Residual Analysis

Interturn stator winding fault is one of the most frequent faults in permanent-magnet synchronous machines (PMSMs). In this paper, we present a new technique for online detection of this fault in PMSMs. It is based on a residual analysis improved by taking into account back-electromotive force waveform estimation, inverter model, and unbalanced inductance matrix. Then, a current residual monitoring block permits to detect the fault and its severity. The simulation and experimental results validate the proposed method and its efficiency.

Measurement and calculation of 3-column 15-winding autotransformer

Measurement and calculation of 3-column 15-winding autotransformer The 15-winding and 3-column autotransformer supplying an 18-pulse rectifier circuit was developed. Presented methods can be used also for the autotransformers of other topologies supplying different kinds of converters. Presented methods make it possible to exactly calculate main and leakage inductances of the multi-winding autotransformer. The presented analysis of the eigenvalues and eigenvectors of the inductance matrix makes it possible to identify the influence nature of individual modes on the inductance matrix, and to compare the calculation results obtained using the presented methods. Frequency dependence of autotransformer parameters was shown. Also modes of the impedance matrix of the multi-winding autotransformer was investigated, this made it possible to identify the influence nature of individual modes on the inductance matrix. Using presented methods one can exactly calculate main and leakage inductances of the autotransformer. Thanks to this, one can design in optimal way autotransformers for supplying, for example, rectifier circuits, THD coefficients. The results of the measurements and simulations were also shortly presented at the end of the article.

Calculating the main and leakage inductance matrix of the 3-column 15-winding autotransformer

Calculating the main and leakage inductance matrix of the 3-column 15-winding autotransformer The aim of this paper is presentation and comparison of calculation methods of the inductance matrix of a 3-column multi-winding autotransformer. Main and leakage autotransformer inductance was obtained using finite elements method. Static calculations were made at the current supply for 2D and 3D models, and mono-harmonic calculations were made at the voltage supply. In the mono-harmonic calculations the eddy current losses were taken into account, this made it possible to study relationship between the autotransformer parameters and the frequency. Calculations were made using Ansys and the authors' own programs in Matlab.

Accurate and Efficient Computation of the Inductance Matrix of Transformer Windings for the Simulation of Very Fast Transients

When a transformer is subjected to very fast front transients, the penetration of the magnetic flux into the core becomes, in general, negligible. To represent this phenomenon, it is common practice to compute the winding inductance matrix (turn-to-turn) at very high frequencies using the expressions for air-core inductors. However, since the core becomes a magnetic insulating wall at very high frequencies (MHz), the distribution of the magnetic field is altered because the field cannot enter the region occupied by the core. Therefore, the air-core approximation formulae overestimate the inductance at high frequencies. This is especially true in the region inside the core window. Large errors are found when the inductances are computed with the air-core approximation. This paper presents a technique, based on the application of a multilayer method of images, to take the presence of the core into consideration. The final expressions are very simple, yet they give remarkably accurate results. Comparisons with finite-element analyses prove the excellent accuracy of the technique.

Closed form Delay Model for on-Chip VLSIRLCG Interconnects for Ramp Input for Different Damping Conditions

Fast delay estimation methods, as opposed to simulation techniques, are needed for incremental performance driven layout synthesis. On-chip inductive effects are becoming predominant in deep submicron interconnects due to increasing clock speed and circuit complexity. Inductance causes noise in signal waveforms, which can adversely affect the performance of the circuit and signal integrity. Several approaches have been put forward which consider the inductance for on-chip interconnect modelling. But for even much higher frequency, of the order of few GHz, the shunt dielectric lossy component has become comparable to that of other electrical parameters for high speed VLSI design. In order to cope up with this effect, on-chip interconnect has to be modelled as distributed RLCG line. Elmore delay based methods, although efficient, cannot accurately estimate the delay for RLCG interconnect line. In this paper, an accurate analytical delay model has been derived, based on first and second moments of RLCG interconnection lines. The proposed model considers both the effect of inductance and conductance matrices. We have performed the simulation in 0.18μm technology node and an error of as low as less as 5% has been achieved with the proposed model when compared to SPICE. The importance of the conductance matrices in interconnect modelling has also been discussed and it is shown that if G is neglected for interconnect line modelling, then it will result an delay error of as high as 6% when compared to SPICE.

A Comprehensive Analytical Mathematic Model for Permanent-Magnet Synchronous Machines Incorporating Structural and Saturation Saliencies

We introduce a new method to model permanent-magnet synchronous machines (PMSMs) with saliencies due to the salient structure and magnetic saturation. We define two parameters to indicate these saliencies, i.e., the structural saliency ratio and the saturation saliency ratio . To verify the nonlinear model, we tested a real PMSM and numerically simulated it. The nonlinear inductance matrix is deduced and expressed by a nonlinear function regressed from the experimental data. The simulation and experimental results agree well with each other.

Sheet current model for inductances extraction and Josephson junctions devices simulation

Sheet current model for microelectronic superconductor structures, based on Maxwell and London equations, is presented. In this model, magnetic field is three-dimensional but resulting integro-differential equations for current density potential are two-dimensional. These equations are solved using finite element method and matrix of self and mutual inductances is calculated as well as current distribution in superconductors. Then, current distribution can be used for calculation of boundary conditions for Josephson junctions equations. In particular we apply this approach for calculations of bias and control line currents for flux flow oscillator simulation problem. The program and results of calculations are presented.

A Vector Impedance Meter Method to Characterize Multiconductor Transmission-Line Parameters

For analyzing and simulating the behavior of multiconductor transmission lines, a measurement of the transmission-line parameters is needed. In this paper, an accurate method for measuring the full capacitance, inductance, resistance, and shunt-resistance matrices by a vector impedance meter is described. The method has been applied for frequencies in a range from 20 kHz up to 30 MHz.

Analyse et conception d’un coupleur coaxial rectangulaire à conducteurs internes circulaires par la méthode des éléments finis

Finite element analysis and design of a rectangular coaxial coupler with circular inners conductorsIn this paper, we present the analysis of rectangular coaxial coupled lines with circular inners conductors. This analysis is based on a numerical resolution of the Laplace's equation by the finite element method (FEM). This technique is adapted to study the complex configuration of the line’s system which does not have simple analytical solution. The modelling of this structure consists in analysing the even and the odd mode characteristic impedances (Zoe, Zoo), the coupling coefficient (k) and the inductance and capacitance matrices ([L] and [C] matrices, respectively). Also we present the results of a directional coupler design. The numerical model developed remains valid to all TEM and symmetrical couplers.

Group-Delay Engineered Noncommensurate Transmission Line All-Pass Network for Analog Signal Processing

A group-delay engineered noncommensurate transmission line two-port all-pass network for analog signal-processing applications is presented, analytically modeled, and experimentally demonstrated. This network consists of transversally cascaded C-sections, which are distributed implementations of the bridged-T equalizer lumped circuit. It is obtained by interconnecting the alternate ports of adjacent lines of a 2N -port coupled transmission line network with transmission line sections, and it is modeled using multiconductor transmission line theory with per-unit-length capacitance matrix C and inductance matrix L. By allowing the different C-sections of the network to exhibit different lengths, a generalized group-delay engineering procedure is proposed, where quasi-arbitrary group-delay responses are achieved by combining the group-delay responses of C-sections with different lengths. A computer design approach based on genetic algorithms is applied for synthesis, which consists of determining the structural parameters of the different C-section groups. Using this approach, noncommensurate networks are group-delay engineered in edge-coupled stripline technology, and Gaussian, linear and quadratic group-delay responses are realized. The theoretical results are validated by experiment. Finally, two application examples of analog signal processing-a tunable impulse delay line and a real-time frequency discriminator-using the proposed dispersive noncommensurate all-pass networks are presented.

Finite-Element Inductance Computation in 2-D Eddy-Current Systems Using Sensitivity Analysis

A new finite-element (FE) method for the determination of differential and apparent inductances of massive conductors is proposed using a sensitivity analysis approach. The new technique is a one-step computation procedure in which the definition of distribution vectors makes possible a unified treatment of solid and filamentary conductors. Since massive conductors are included in the formulation, eddy-current and proximity effects are properly considered. The inductance matrix expression, formally derived from the sensitivity analysis, requires only one evaluation of the Jacobian matrix of the FE system at the solution point. As a result, an efficient calculation can be performed using the same solver employed in the FE solution. The computation of a multiport equivalent of an induction machine has been used to show the power of the proposed method. Our FE and multiport network results have been validated using a well-known commercial FE package.

An improved algorithm of finding steady‐state solutions for AC machines

PurposeThe purpose of this paper is to reduce issues arising when computing steady‐state solutions for AC machine models using the harmonic balance method.Design/methodology/approachGenerally, currents at steady‐states of AC machines are described by periodic or quasi‐periodic time functions, which Fourier spectra are determined by an infinite set of algebraic equations obtained from a harmonic balance method. To solve them, after reducing to finite dimensions, an iterative algorithm is developed in this paper. It bases on the LU decomposition of an infinite matrix representing the inductance matrix of an AC machine. Since that decomposition is done separately, due to a band type form of this matrix, the equation set determining the Fourier spectra of currents is solved recurrently.FindingsAn algorithm for the LU decomposition of an infinite matrix representing the inductance matrix of an AC machine and an iterative algorithm for determining AC machine steady‐state currents in a recursive manner.Research limitations/implicationsThe approach is limited to solving of so‐called “circuital” models of AC voltage supplied machines. The approach breaks the large dimension barrier when solving steady‐state equations for AC machines.Practical implicationsReducing computer requirements in terms of computer memory, workload and computing time to determine a steady‐state solution for AC machines.Originality/valueA separation of the LU decomposition of an infinite matrix representing the inductance matrix in AC machine steady‐state model from the solution method.

Correction of the Method of Images for Partial Inductance Calculations of QFP

The inapplicability of the method of images to partial inductance calculation within the magneto-quasi-static approximation has been shown by the authors in previous works. This concept is restated in this paper, and some correction terms for the application of the method of images are proposed. A partial inductance calculation technique based on potential theory is also proposed, which does not require the calculation of the current distribution, and is limited at present to infinite perfectly conducting planes. The proposed correction terms are verified with simple structures at first, and later with the calculation of the partial inductance matrix of a quad flat package.

Generating Stable and Sparse Reluctance/Inductance Matrix under Insufficient Discretization

This paper presents generating stable and sparse reluctance/inductance matrix from the inductance matrix which is extracted under insufficient discretization. To generate the sparse reluctance matrix with guaranteed stability, the original matrix has to be (strictly) diagonally dominant M matrix. Hence, the repeated inductance extractions with a smaller grid size are necessary in order to obtain the well-defined matrix. Alternatively, this paper provides some ideas for generating the sparse reluctance matrix, even if the extracted reluctance matrix is not diagonally dominant M matrix. These ease the extraction tasks greatly. Furthermore, the sparse inductance matrix is also generated by using double inverse methods. Since reluctance components are not still supported in SPICE-like simulators, generating the sparse inductance matrix is more useful than the sparse reluctance one.

General Analytical Models of Inductance Matrices of Four-Pole Bearingless Motors With Two-Pole Controlling Windings

In this paper, after introducing the bearingless motor's working principle in brief, we analyze the magnetic field distribution principle of the bearingless motor. We then derive in detail the general analytical models of inductance matrices of a four-pole bearingless motor with two-pole controlling windings. The derived general analytical models are applicable not only to bearingless motors with a salient-pole rotor, but also to bearingless motors with a cylindrical rotor. By setting different values of salient-pole arc width parameter rho in the general models of inductance, the analytical models of inductance of different types of bearingless motors, such as bearingless induction motors, bearingless synchronous reluctance motors, and bearingless surface-mounted permanent magnet (SPM) motors, can be derived.

A Simple Derivation of Microstrip Transmission Line Equations

A simple asymptotic approximation that describes the electromagnetic fields, currents, and voltages in a general microstrip transmission line problem is presented. Specifically, the transmission line equations relating the currents and voltages are established in a very efficient manner. Important properties of the capacitance and inductance matrices are established using elementary mathematics. These results and the equations are general enough to describe any number of microstrips, whose widths are allowed to vary in direction of propagation. When the widths are constant in this direction, another elementary asymptotic approximation shows that the electromagnetic fields are exponentially small away from the strips. This is, of course, the feature that makes them useful in guiding waves.

Effect of external electromagnetic waves on a confocal elliptical multiconductor transmission line structure

The influence of external electromagnetic waves on a new kind of transmission line called a confocal elliptical multiconductor transmission line structure is introduced. The capacitance and inductance matrices are obtained to attain transmission line equations. Then a uniform plane wave, TEz or TMz mode, is applied to the structure (normal incidence) to find the induced voltages and currents along the conductors using Bernardi's method. Finally, the results of this analytical method are verified using the fullwave analysis software.

EM FIELD COUPLING TO NON-UNIFORM MICROSTRIP LINES USING COUPLED MULTI-CONDUCTOR STRIPS MODEL

A model for the two-dimensional analysis of microstrip lines, named Rigorously Coupled Multi-conductor Strip (RCMS) is introduced. In this model, the width of the strip of a microstrip line is subdivided into a large number of rigorously coupled narrow strips. So, a microstrip line can be considered as a coupled multi-conductor transmission line. Determination of the capacitance and inductance matrices of the model is introduced, also. The voltages and currents induced by electromagnetic flelds for the coupled multi-condutor strips problem can be obtained using Bernardi's method. The efiect of an external EM wave on a microstrip line with non-uniformity in its width is computed by adding the circuit model of transverse discontinuity (narrow slit) to the RCMS model. Finally, the validity and e-ciency of the introduced method is investigated using previous work and full wave EM-simulation software.

Derivation of free-boundary equilibrium linear models by a flux perturbation method

A new method to derive linear models of the axisymmetric plasma dynamic is detailed. The method follows the modified inductance approach but adopts a different set of independent variables to perturb the equilibrium. This different basis permits one to reduce the numerical computation of the model and has revealed an interesting property of the inverse inductance matrix whose elements are influenced by the plasma only if they refer to circuits facing directly the plasma column. In terms of approximations, the method proposed is equivalent to the standard modified inductance method but has the additional advantage of ensuring numerical convergence of the perturbed equilibria and therefore it allows using Picard based numerical Grad–Shafranov solvers. A linear model of the RFX-mod machine was derived with this approach and it was validated against the experiment.

Implementation and verification of the Hybrid Transformer model in ATPDraw

The paper documents a new transformer model in ATPDraw called XFMR. This model handles three-phase transformers with two or three windings. Autotransformers and all Wye and Delta couplings are supported. The model includes an inverse inductance matrix for the leakage description, optional frequency dependent winding resistance, capacitive coupling, and a topologically correct core model (3- and 5-legged) with individual saturation and losses in legs and yokes. Three different sources of parameters are supported; typical values, standard test reports, and design information. The hybrid model XFMR is compared to the UMEC model in PSCAD showing good agreement at rated, stationary operation, but considerable differences in transient situations. Both models need further benchmarking and development to reproduce all switching transient behaviors properly.