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1

Transients in Transformers with Non-Uniform Inductance and Capacitance Distributions

Saied M. M.

Electrical Power Quality and Utilisation. Journal

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2017

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Vol. 20, no. 1

7--14

EN

The electromagnetic transients in transformer windings exhibiting location–dependent inductances and capacitances are investigated in the time domain. Analytical functions describing this dependence are assumed and incorporated in the two integro–differential equations governing the transient voltage and current distributions. The boundary conditions are available from the source initiating the transients and the winding’s end termination. A numerical procedure is applied in order to get frequency domain solutions for the voltage and current in the form of Interpolating and Parametric Functions. The numerical Laplace inversion is then applied to these s–domain expressions. Results pertinent to transients initiated by step- and double-exponential impulse sources are presented and discussed. All possible transformers’ neutral connections are considered. The possible error introduced by neglecting either or both of the inductance and capacitance non-uniformities is addressed. Results indicate that the main error is attributed to neglecting the inductance non-uniformity, whereas the impact of the capacitance non-uniformity is relatively small. In most cases, the winding’s copper and insulation losses have a small effect on the transient response.

2

Transformer Modelling for the Frequency and Transient Analyses, with Non-Uniform Inductance Emulating the Inter-Turn Magnetic Coupling

Saied M. M.

Electrical Power Quality and Utilisation. Journal

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2014

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Vol. 17, iss. 1

1--11

EN

A new procedure for analyzing power transformer windings with location-dependent circuit parameters, such as the series inductance, is presented. This dependence is introduced in order to take the inter-turn mutual inductive coupling into consideration. It can be expressed either by analytical expressions or even in a tabulated form. The paper addresses both the frequency and time domain analyses. They are based on replacing the winding by an adequate number of equivalent cascade connected two-ports. In contrast to the usual practice of applying the simple medium line representation, each of these two-ports is treated as a long transmission line. Their A, B, C, D generalized circuit constants will be therefore generally location-and frequency-dependent. The analyses will be conducted in the complex s-domain. The corresponding time-domain results can then be obtained by applying a numerical inverse Laplace transform. Expressions for the winding’s input impedance with different treatments of the transformer’s neutral point will be derived for any assumed number of the equivalent two-ports. Results pertinent to the frequency characteristics including the resonance frequencies are presented. The paper also describes the winding’s transient response to the application of two standard voltage stimuli. The suggested approach is validated by its application to a case study for which an analytical closed-form solution is available. The analysis of windings exhibiting nonuniformities in more than one equivalent.

3

Studies on abundance in selected nutrients of differently used soils derived from loess

Ciarkowska K., Sołek-Podwika K.

Ecological Chemistry and Engineering. A

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2008

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Vol. 15, nr 1-2

29-34

EN

One of the factors determining soil fertility is the content of nutrients, easily available for plants. The objective of the work was the assessment of the effect of the soil use on the content of nutrients and the evaluation how their content is in geologically uniform loess soils and non-uniform underlain with sand. As a result of studies it can be ascertained that agricultural practices performed on arable lands contributed to enrichment in phosphorous available for plants in humus horizons. Surface horizons of arable lands and meadows were characterized also by a higher content of available magnesium and exchangeable magnesium and potassium in comparison with forest soils. When sand bedrock underlying loess lowered the nutrient abundance in non-uniform soils.

PL

Jednym z czynników warunkujących żyzność gleby jest zawartość składników pokarmowych występujących w formach dostępnych dla roślin. Celem pracy była ocena wpływu sposobu użytkowania gleby na zawartość składników biogennych oraz określenie, jak kształtuje się ich zawartość w glebach lessowych całkowitych oraz niecałkowitych podścielonych piaskiem. W wyniku przeprowadzonych badań stwierdzono, że zabiegi uprawowe na gruntach ornych przyczyniły się do wzbogacenia poziomów próchnicznych gleb w fosfor przyswajalny dla roślin. Poziomy powierzchniowe gruntów ornych i gleb łąkowych charakteryzowały się również większą zawartością przyswajalnego dla roślin magnezu oraz wymiennych form magnezu i potasu w porównaniu z glebami leśnymi. Podłoże piaszczyste lessu wpłynęło natomiast na pogorszenie zasobności pierwiastków biogennych tych gleb.