- مبلغ: ۸۶,۰۰۰ تومان
- مبلغ: ۹۱,۰۰۰ تومان
In this paper, resonance effects in transformer windings are thoroughly investigated and analyzed. The resonance isdeterminedbymakinguse of anaccurate approachbasedonthe applicationofthe impedance matrix of a transformer winding. The method is validated by a test coil and the numerical results are verified by an ATP-EMTP model. Further analysis is applied on a transformer winding for which the inductance and the capacitance matrix as well as the winding losses are previously determined. By having determined the amplification factor, it can be found the location where the most severe transients may occur. It is also shown that maximum resonance overvoltage depends on the duration of the excitation and its resonance frequency.
The paper presents a comprehensive and detailed analysis of resonance effects intransformers. The analysis isperformedononly one transformer phase, however,the approach is generally applicable for any transformer as long as the inductance and capacitance matrix as well as losses are accurately determined. It is valid for multi-winding multi-phase transformers with any type of wind- ing. Z matrix of transformer windings contains all the information about the voltage and current distributions in the winding. The transformer saturation in this case is nottaken into account. However, since the impedances are computedinfrequencydomain, the influence of the core can also be taken into account. Anyhow, experience shows that the core has limited influence up to several tens of kilohertz. This has been validated by measurements on open and short circuited secondary winding of the transformer . The applied parameters, which are explained in more detail in Ref.  are computed in a way that the flux does not penetrate the core. Experience and previous work reveals that above several tens of kilohertz this is justified. In this work, it is shown that the voltage distribution for existing resonance frequencies can be determined by computing the amplification factor based on the provided characteristics. Here, only one resonance frequency was analyzed. Voltage distributions for different resonance frequencies can be calculated in the same way. This analysis has also shown that another crucialfactor, which influences overvoltage amplitude is the excitation duration. When a transformer is exposed to resonance oscillations for a longer time, the value of the maximum amplification factor of some coil can be reached. Finally, lossy frequency dependent inductances obtained by Wilcox’s approach  can be used to represent transformer frequency-dependent losses and inductances. On one hand, the representation of these matrices in EMTP-based environment is possible by making use of constant parameters for the resistances and inductances. On the other hand, this is not fully accurate since frequency-dependency isnottakeninto account. One solution regarding this issue is to define the validation of these parameters for particular frequency range and make use of such model for particular bandwidth. EMTP-based approach can be very useful since once the model is built, it can be used in a bigger network. However, some preparations to generate a suitable EMTP-based model are necessary. Since the inductances, resistances and capacitances cannot be included in EMTP environment as frequency dependent, it is important to perform sensitivity analysis in order to see how close the terminal harmonic impedance matches the one computed as suggested in Section 2.