Interfacing <formula formulatype="inline"><tex Notation="TeX">${\rm k}$</tex></formula>-Factor Based White-Box Transformer Models With Electromagnetic Transients Programs

Abstract

White-box transformer models are used by transformer manufacturers during the dielectric design of windings. The models are often based on constant parameters (RLCG matrices) with the high-frequency losses accounted for by a scaling of the dc resistance ( -Factor). We show an efficient procedure for interfacing such models with Electromagnetic Transients Program (EMTP)-type circuit simulators via state equations and a Norton equivalent. The approach makes no approximations except for the discretization in the time domain. Diagonalization is utilized for achieving high computational efficiency. Proprietary information about internal voltages is optionally hidden from the user. Internal surge arresters are handled by the EMTP circuit solver by declaring their connection points as external nodes. The model interface includes automated initialization from 50/60-Hz initial conditions. The proposed interfacing capability permits manufacturers to apply their models in complete network simulations, and to share their models with users.

Rational Function Approximation of Transformer Branch Impedance Matrix for Frequency-Dependent White-Box Modeling

“…The internal connections and groundings are handled by a modification to the matrices of G , C , and T as described in Appendix B of [6].…”

“…It is assumed that a node reordering has been made so that the external nodes come first. Such reordering is conveniently achieved using a node-reordering matrix [6]. The current injections now take place at the first (few) external nodes,…”

“…and inductance B L , and shunt capacitance C and conductance G [5]. Such models can be formulated on state-space diagonal form and be directly interfaced with EMT programs as shown in [6] and [7], or via a black-box modeling approach [8]. An alternative approach is to interface the model via a large, equivalent electrical circuit representation [9].…”

“…These daily-use models have the advantage that the model parameters can be calculated very efficiently using analytical formulae [5]. The losses can, as a first approximation, be included by calculating the branch impedance resistance matrix B R at a fixed frequency, giving a k-factor model [6]. It has been found [5], [10] that the daily-use models often have accuracy shortcomings when applied in general transient studies, in particular if one wishes to simulate the internal voltages that can occur in resonant situations, e.g.…”

Time-Domain Implementation of Damping Factor White-Box Transformer Model for Inclusion in EMT Simulation Programs

“…we finally calculate the history current source vector using (11) and the internal node voltages using (10b). This initialization scheme is much simpler than the approach in [13] which makes use of complex-valued state variables in the time domain. It is remarked that the adopted implementation is in principle similar to that used for linear branch elements in existing EMT programs [14].…”