# The Influence of Capacitance and Inductance Changes on Frequency Response of Transformer Windings
## 5 Conclusions  
This paper provides the analysis of the influence of capacitive and inductive parameters on the frequency response of transformer windings. The FRA method is one of the important test methods of power transformers, being a part of advanced diagnostics. The interpretation of measured data is not always easy, especially in cases where two compared curves (i.e., measured in the same test setup in time intervals) differ in some frequency ranges. The question is if such a difference is related to deformation or electric fault in the windings, or maybe it has its source in some additional effects.  
The first aim of the paper was to prepare a computer model of a transformer that would allow for analysis of capacitance and inductance changes on the frequency response. The results of modeling showed that changes of inductance of the winding or changes in capacitive parameters have an influence on FR curve. It can be seen as the frequency shifts of FR. Such an influence was expected, however combination of changes in these parameters may lead to misleading effects on the shape of FR characteristics. It was shown in modeling results that capacitance has its influence in the LF range, while inductance changes influence FR curve in the wider range. The second aim of the paper was to provide results from industrial measurements that would verify conclusions obtained from the model. There are two groups of such results presented: measured for different positions of OLTC, and with an additional capacitor installed on bushings in phases other than those tested. It can be seen that some differences between two compared curves, measured for the same unit, which are visible in MF range and related to local deformations, may be the effect of inductance changes (e.g., different tap positions for both measurements). The verification of such a measurement mistake by observing the LF range may be misleading if additional capacitive effects cover the inductive effect, or if the core of a transformer was magnetized by earlier DC measurement.  
Practical measurement values of changes of inductance or capacitance, which influence the shape of FR, are unknown. In addition, each transformer construction has a different FR curve shape, in which the position and number of resonances are different, therefore the influence of \(C\) and \(L\) parameters can appear in a different way. This makes it difficult to give one universal method for detection of these changes (e.g., a simple formula), which were described in this paper, but it is easy to analyze characteristic behavior in given frequency ranges, which are related to \(L\) and \(C\) changes. For example, the capacitance change influence of FR ends above 5-10 kHz. This value depends on the geometrical size of the unit (related to the power rating and nominal voltages). The problem of finding universal markers for detecting inductance or capacitance changes will be the aim of further research.  
The paper presents analysis that can be used in the assessment of FRA measurement, especially in the case of uncertain data comparison results.  
Conceptualization, S.B.; methodology, S.B., K.M.G., K.T., and P.B.; resources, S.B.; supervision, S.B.; visualization, S.B. and K.T.; writing--original draft, S.B., K.M.G., K.T., and P.B.; writing--review and editing, S.B. and K.M.G.  
The authors declare no conflict of interest.