###### Abstract  
One of the standard diagnostic methods for power transformers is frequency response analysis (FRA). This paper deals with progress in the frequency response interpretation of these very important appliances in the power network. Simulations of the frequency response of the transformer windings are a useful way to improve the correct assessment of FRA results. One of the disadvantages of FRA modelling is time-consuming analysis, especially of large multilayer windings. The aim of this article is to develop a numerical model, which would reduce the duration of the electromagnetic field analysis of the winding with hundreds of turns. The approach introduced in the paper describes the simple two-dimensional (2D) finite elements method (FEM) model, which provides the results comparable to the three-dimensional (3D) model. Moreover, the paper presents the numerical models, which demonstrate the influence of the remaining windings on the inductance of tested winding. As a result of the conducted research, the comparison of inductance curve obtained from FRA measurement on the physical model with modelled resonance slope is presented, both for 2D and 3D cases. f 2020 202  
the FRA results is finding the right correlation between curve deviations and damages of the measured winding. Correct analysis of the frequency response (FR) results requires taking into account several factors, including winding geometry, the history of failures, or the connection system. Temperature and moisture content also influence the frequency response of the transformer winding, shifting the FRA spectrum horizontally [7]. Often, the visible changes in two compared curves are not a consequence of deformations in the tested winding, but may come from other components of the transformer [8; 9; 10]. Consequently, researchers are developing tools, which could help evaluate the FRA test results, including statistical methods [11; 12] and methods based on the artificial intelligence [13; 14]. One of the possibilities to improve the correct assessment of the FRA results is a simulation of the frequency response. The reason for using the computer models in the assessment of the FRA results is to explain how mechanical faults change the frequency response. In practice, because of high costs of experiments on the real units, the enhancement of a FRA database for the transformers' active part faults is possible only in the way of numerical simulations (Figure 1) [15]. Recent studies have focused on models that reproduce the FRA signature as close as possible and allow free access to the winding parameters. There are several approaches to establish this goal: mathematical models [16; 17], models based on finite element analysis (FEM) [18; 19; 20], and equivalent electrical circuit models, in particular lumped parameters circuit models [21; 22; 23; 24]. In current FRA research, the lumped parameters circuit models are widely used to examine the behaviour of the FR of the windings. Although these models combined with the FEM electromagnetic field analysis give satisfactory results, there are many issues that need to be refined in simulations of the FR. One of the problems is the issue of the complexity of multilayer windings with hundreds or thousands of turns. Even small changes in RLC parameters of the tested winding are visible in FRA signature; hence, it is significant to conduct the field analysis as accurately as possible. On the other hand, the three-dimensional (3D) field analysis, taking into consideration the skin-effect in windings, requires very dense meshing. The numerical analysis of such a model is complicated and very time-consuming. The analysis can be simplified by using some approximations, which will allow us to handle the frequency-dependent effects in core material. Another way to increase the FEM analysis efficiency is to develop the two-dimensional (2D) model, what will correspond with the 3D model in high accuracy.