Impact of hysteresis phenomena in time and frequency analysis for inrush currents in power transformers

Abstract

The first energization of a power transformer in an energy distribution system is a critical issue in the transformer’s lifetime since the high currents experienced by the device in these conditions. Such currents are primarily due to magnetization of the iron core, which exhibits memory phenomena and saturation. Further, the initial phase strongly affects dynamics and could push the core in a saturation state, which, in turn, reduces the primary coil impedance and hence enables the current to rise (up to 10-15 times the full load current). This transient current is usually referred to as inrush current [1,2] and can be very dangerous for the device, causing electrodynamic stress, dissipations and consequent heating of the electrical insulations, harmonics production and their circulation in the power system. Such magnetizing currents focused great attention in the analysis of large transformers.The latest research activity was basically focused on the modeling, at the macroscopic scale, of the magnetization processes taking place in the transformer’s core, strongly affecting the circuit’s dynamics. The effort was therefore aimed to plug into the circuit model a suitable hysteresis operator. Different proposals discussed the effects of hysteresis models (e.g., Preisach, Jiles Atherton (J-A), etc., [3,4]) on the global behavior of the transformer dynamics, with particular emphasis to model’s accuracy and computational weight, [5,6].The J-A model offers a tool to describe hysteresis, but it is able to describe too simplified memory phenomena, [3] and requires a nontrivial parameters identification (e.g., through a nonlinear optimization). Conversely, Preisach model (PM) provides a memory description that fits with the real macroscopic processes but requires some expertise and a large of measured data (i.e., first order reversals), which limits its use in non-specialized frameworks, as power circuits and industrial electronics.Therefore, the availability of well-behaved hysteresis operator suitably simplified with respect to, e.g., the Preisach model, would represent an interesting contribution to this field.In the present contribution, the core magnetization modeling of a power transformer in a network is provided through a Preisach-based operator (i.e., it is characterized by the Preisach memory updating rules), [7] offering a simpler implementation, inverse operator availability and a reduced set of measured data, than PM. Such operator, as detailed hereafter, is based on a weighted linear superposition of elementary operators (Play operators, see, [7]) and will be referred to as Prandtl-Ishilinskii (P-I) operator. Further, due to its simpler structure and reduced numbers of parameters, it allows the inrush current process analysis in a wide range of magnetization conditions with low effort.The P-I model, describing the B-H characteristic, along with the circuit’s equations, referred to the same circuit as in [6], are reported in Fig. 1. In the first frame, Pr[.] is the play operator, while μ(r) is a weight function and the saturation magnetization, Ms = 1.5T. In the second frame, R1 is the primary resistance, E the voltage amplitude, while F is the hysteresis operator linking the flux linkage to the primary current. The secondary current is assumed zero during the analysis.The model so conceived is able to fairly describe the behavior of a realistic core, as shown in the same figure.The circuit’s behavior has been preliminary tested in the same conditions as in [6]. However, in Fig. 2 its behavior has been studied in conditions where the great arise of (inrush) currents clearly appears. In the same figure the impact of hysteresis with respect to a memoryless description is outlined.Aim of the paper will be a thorough testing of the proposed model, in terms of accuracy, computational efficiency for the analysis of inrush currents phenomena in power transformers. The characteristics of the hysteresis operator would allow an immediate analysis of the basic magnetic parameters affecting the inrush currents dynamics. In particular, the influence of remanence, coercive field and permeability at current reversal, will be investigated.For the latter (initial permeability at the branch start), during the transient, the material experiences an up and forth current variation, allowing the branching to arise and to affect (in the starting part of the branch characterized by low permeability) the whole current dynamics. Such effect, which strongly relies on the initial magnetization state of the iron core (Mr), could be easily described by the proposed model and of course, cannot be taken into account when a nonlinear memoryless modeling is employed. **