Poenostavljena metoda upoštevanja dinamičnih histereznih izgub v modelu enofaznega transformatorja - Deželak, Klemen (Elektrotehniški vestnik, 2007)
The paper deals with, a magnetically nonlinear dynamic model of a single-phase transformer where the effects of dynamic hysteresis losses and iron core losses to be accounted for by a simplified method. The existing simplified method 4 for considering dynamic iron core losses in the form of magnetizing curve B(H), displaced to the left and to the right by factor Hhist (22), is modified. It is now suitable to be used when the magnetizing curve of the iron-core material is not available, while the magnetically nonlinear characteristic y(i) of the entire device can be determined experimentally 7. The characteristic y(i) can be given in the form of an approximation polynomial or in the form of a look-up table. A schematic presentation of the discussed single-phase transformer is shown in Figure 1. It is used as a basis for two different circuit models presented in sections 2.1 and 2.2. The first circuit model with neglected eddy-current losses is shown in Figure 2, while the second circuit model with the eddy-current losses are accounted for by the resistor RFo is shown in Figure 3. The corresponding magnetically nonlinear single-phase transformer dynamic models is given by sets of equations (1) to (11) and (12) to (20). In the first model, only the hysteresis losses can be accounted for while the second one can handle hysteresis and eddy current losses. Both models are completed by magnetically nonlinear characteristic y(i) of the tested transformer. Section 3 describes how the hysteresis losses can be accounted for by shifting an unique magnetically nonlinear iron - core characteristic given in the form of the magnetizing curve B(H) to the left and to the right by factor Hhist. The complete approach is explained in Figure 4 where fo denotes the unique characteristic B(H). Factor Hhist (22) is defined by the hysteresis factor Khist, actual flux density B and flux density in the last turning point Brev. Equations (23) to (25) show, how partial derivatives a&ao, needed in dynamic models (equations sets (1)-(1 1) and (12)-(20)), can be determined from characteristic B(H). Expressions (26) and (27) are used to determine characteristic VI(i) from the measured applied voltage and corresponding current under transformer no-load operation. Figure 5 shows a set of characteristics VI(i) in the form of hysteresis loops determined for different amplitudes of the applied voltage. The unique characteristic y(i) used in calculations is given by end points of individual hysteresis loops. Equations (28) to (31) are used to determine magnetic reluctances Rm or partial derivatives Mao from the end points of the individual hysteresis loops shown in Figure 5. Figure 6 shows the measured hysteresis loop a), unique y(i) characteristic b) and approximation of the hysteresis loop used to account for hysteresis losses c). A corresponding comparison of the measured and calculated currents is shown in Figure 7. Figure 8 shows that a better agreement the between measured and calculated currents can be achieved if hysteresis losses are accounted for in the transformer dynamic model together with the eddy-current losses.
Keywords: elektroenergetika; transformatorji; modeli; histerezna zanka; izgube