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Open access

Damian Mazur and Marek Gołębiowski

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.

Open access

Damian Mazur and Marek Gołębiowski

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.

Open access

Marek Gołębiowski

Abstract

In this paper the MTPA, MTPF, constant torque and constant flux control trajectories are presented. These trajectories are calculated for a 6-phase asymmetric insettype SMPMSM generator with the assumption of a certain level of 3rd harmonic current injection. This injection technique increases the generator performance due to the cooperation of the fundamental and 3rd harmonic. The presented trajectories are used for fast control of the generator working in the gearless wind turbine system.

Open access

Marek Gołębiowski

Abstract

The presented systems with magnetically coupled windings are solved with the finite element method. If the issue of voltage supply is analyzed, a system of linear equations with a partially skew-symmetric sparse matrix is obtained. Iterative methods used to solve a system of equations are particularly effective for symmetric matrices. Resultant equations can be reduced to this symmetrical form by using the method known from the literature [1]. The ratio of the maximum to the minimum eigenvalue of the main matrix of this circuit, which is the condition number, is however very high. This means that the problem is ill-conditioned and leads to a very long iterative solution process. The method presented in the article allows for a direct solution of a system of equations on its part, corresponding to high eigenvalues of the system matrix. The remaining part of the system of equations is solved by iterative methods. This part has much better condition number, and therefore the computational process is fast. The proposed iterative process depends on multiplication of a sparse matrix by vectors. It is not necessary (and possible) to store the entire matrix. This is especially important for larger sizes of a matrix.

Open access

Christoph Schmuelling, Christian Kreischer and Marek Gołebiowski

Abstract

Commonly, the Park model is used to calculate transients or steady-state operations of synchronous machines. The expanded Park theory derives the Park equations from the phase-domain model of the synchronous machine by the use of transformations. Thereby, several hypothesis are made, which are under investigation in this article in respect to the main inductances of two different types of synchronous machines. It is shown, that the derivation of the Park equations from the phase-domain model does not lead to constant inductances, as it is usually assumed for these equations. Nevertheless the Park model is the most common analytic model of synchronous machines. Therefore, in the second part of this article a method using the evolution strategy is shown to obtain the parameters of the Park model.

Open access

Lesław Gołębiowski, Marek Gołębiowski, Damian Mazur and Matthias Humer

Abstract

In this paper a system of a grid side and a generator side converters, both working with a common capacitor, is presented. The 6-phase asymmetric inset-type SMPMSM generator is used. A large pole pair number of this generator enables a gearless wind turbine operation. The fundamental and 3rd harmonic cooperation is used to increase the generator performance. This is accomplished by means of the 3rd harmonic current injection. For that reason the generator side converter must have a neutral connection.