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## Determination of slot leakage inductance for three-phase induction motor winding using an analytical method

### Abstract

The article introduced some expressions for self- and mutual slot leakage inductance of phase windings for the mathematical model of an induction machine in the natural phase coordinate system and for dq0 model and in an arbitrary coordinate frame. Calculation of self- and mutual slot leakage inductance have been performed for threephase double-layer, delta and delta-modified winding connections. Introduced expressions may be useful in the design of windings and in the analysis of dynamic states of AC electrical machines.
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## Influence of constructional turbo-generator end region design on end winding inductances

### Abstract

The paper introduces a comprehensive investigation in end winding inductances of large two-pole turbo-generators. With the aid of an analytic-numeric approach, where Neumann's formula is applied, the influence of geometric characteristics of double-layer stator end windings with involute shape is analysed. This parameter study results in approximation formulas for the stator self and mutual inductances at stand level as well as for the common used end winding leakage inductance. In order to consider field affecting components as pressure plate, flux shield, rotor shaft and rotor retaining ring, finite elements models for two machines (250 MVA and 1150 MVA) are created and computed. The results are integrated in the developed approximation formulas. Finally the simulation results of machine 1 are compared to the data of two different measurements. All approaches introduced in this paper show good correlation. The high speed of the analytic-numeric calculation is combined with the accuracy and opportunity to consider field affecting components within the extensive finite element computation successfully.
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## Calculating the main and leakage inductance matrix of the 3-column 15-winding autotransformer

### Abstract

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.
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## Measurement and calculation of 3-column 15-winding autotransformer

### Abstract

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.
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## A transformer winding deformation detection method based on the analysis of leakage inductance changes

### Abstract

The detection of transformer winding deformation caused by short-circuit current is of great significance to the realization of condition based maintenance. Considering the influence of environment and measurement errors, an online deformation detection method is proposed based on the analysis of leakage inductance changes. First, the operation expressions are derived on the basis of the equivalent circuit and the leakage inductance parameters are identified by the partial least squares regression algorithm. Second, the amount of the leakage inductance samples in a detection time window is determined using the Monte Carlo simulation thought, and then the samples in the confidence interval are obtained. Last, a criteria is built by the mean value changes of the leakage inductance samples and the winding deformation is detected. The online detection method considers the random fluctuation characteristics of the leakage inductance samples, adjust the threshold value automatically, and can quantify the change range to assess the severity. Based on the field data, the distribution of the leakage inductance samples is analyzed to obey the normal function approximately. Three deformation experiments are done by different sub-winding connections and the detection results verify the effectiveness of the proposed method.
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## Field-circuit modelling of an advanced welding transformer with two parallel rectifiers

### Abstract

The new topology of three-winding welding transformer is proposed. Each secondary winding is connected in parallel through the separate bridge rectifier to the welding arc. The main feature of the proposed device is parallel working of two secondary windings with different rated voltage. The advantage is nonlinear transformation ratio of current that provides unprecedented power efficiency. The self- and mutual leakage inductances, which are important in power conversion, are calculated by 2D FEA model. The operational current of the device is modelled numerically via P-Spice simulator. The proposed topology is up to 30% more power effective than conventional welding transformer provided that the leakage inductances of primary and secondary windings are correctly fitted. This transformer is used for manual arc welding.
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## A Transformer Class E Amplifier

### Abstract

In a high-efficiency Class E ZVS resonant amplifier a matching and isolation transformer can replace some or even all inductive components of the amplifier thus simplifying the circuit and reducing its cost. In the paper a theoretical analysis, a design example and its experimental verification for a transformer Class E amplifier are presented. In the experimental amplifier with a transformer as the only inductive component in the circuit high efficiency ηMAX = 0.95 was achieved for supply voltage VI = 36 V, maximum output power POMAX = 100 W and the switching frequency f = 300 kHz. Measured parameters and waveforms showed a good agreement with theoretical predictions. Moreover, the relative bandwidth of the switching frequency was only 19% to obtain output power control from 4.8 W to POMAX with efficiency not less than 0.9 in the regulation range.
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