Power Transformer Modeling for Inrush Current Calculation

The paper documents a new transformer model in ATPDraw called XFMR. This model handles 3-phase transformers with two or three windings. Autotransformers and all Wye and Delta couplings are supported. The model includes an inverse inductance matrix for the leakage description, optional frequency dependent winding resistance, capacitive coupling, and a topologically correct core model (3and 5-legged) with individual saturation and losses in legs and yokes. Three different sources of parameters are supported; typical values, standard test reports, and design information. The hybrid model XFMR is compared to the UMEC model in PSCAD showing good agreement at rated, stationary operation, but considerable differences in transient situations. Both models need further benchmarking and development to reproduce all switching transient behaviors properly. Contribution The transformer model described in here can, to some extent, be considered as the state-of-the-art in low-frequency transformer model and constitute the starting point for this work. The main contribution of this paper in connection with this work is to emphasize the main weaknesses of two transformer models: the accuracy of the response in complete saturation and the representation of remanence. [Pb3] Transformer Short-Circuit Representation: Investigation of Phase-ToPhase Coupling Abstract Transformer short-circuit behavior is typically represented in electromagnetic transient simulation programs by the inverse of the leakage inductance matrix, also known as the A-matrix or [A]. The terms of [A] represent the magnetic coupling (flux linkages) between windings, i.e. between coils on the same core leg. In addition to the representation of coupling between windings of the same phase, intraphase coupling effects can also be included. This paper investigates the sensitivities of results of EMTP-type simulation to intra-phase entries of [A]. A method for obtaining [A] that includes intra-phase coupling is developed and verified by comparing simulation results with laboratory measurements. The percent error between measured and simulated short-circuit currents that result from implementing a full and simplified [A] was quantified. A correlation of the size of the elements representing intra-phase coupling in [A] with transformer MVA size is investigated and valuable conclusions and recommendations are made. Contribution The main contribution of this work is the verification that intra-phase entries of [A] are small as the contribution from phase-to-phase leakage fluxes is insignificant. The phase-to-phase coupling can therefore be assumed concentrated in the transformer core and the leakage representation decoupled for the three phases. -92Transformer short-circuit behavior is typically represented in electromagnetic transient simulation programs by the inverse of the leakage inductance matrix, also known as the A-matrix or [A]. The terms of [A] represent the magnetic coupling (flux linkages) between windings, i.e. between coils on the same core leg. In addition to the representation of coupling between windings of the same phase, intraphase coupling effects can also be included. This paper investigates the sensitivities of results of EMTP-type simulation to intra-phase entries of [A]. A method for obtaining [A] that includes intra-phase coupling is developed and verified by comparing simulation results with laboratory measurements. The percent error between measured and simulated short-circuit currents that result from implementing a full and simplified [A] was quantified. A correlation of the size of the elements representing intra-phase coupling in [A] with transformer MVA size is investigated and valuable conclusions and recommendations are made. Contribution The main contribution of this work is the verification that intra-phase entries of [A] are small as the contribution from phase-to-phase leakage fluxes is insignificant. The phase-to-phase coupling can therefore be assumed concentrated in the transformer core and the leakage representation decoupled for the three phases. -92i i “PhDThesis” — 2010/5/28 — 14:59 — page 93 — #111 i i