# The Influence of Capacitance and Inductance Changes on Frequency Response of Transformer Windings
## 1 Introduction  
Transformers play a major role in power distribution systems. They are expected to be in operation for at least 30 years, sometimes even in very unfavorable conditions. One of the key values in power distribution is availability, as its increased value over longer timespans translates into less total distribution costs for operators and an increase in the volume of energy sales. When it comes to older units, owners often have to decide whether to further operate them with some technical restrictions, schedule major maintenance, or withdraw the from further operation and replace them with new units. During their lifetime, transformers undergo maintenance and measurements to assess their technical condition. The basic measurements do not require transformers to go offline for a long period of time, therefore they are commonly used. The advanced methods are used much less frequently (usually once in a couple of years), since they are costly and more time-consuming. Regular, comprehensive measurements, however, give users detailed information about the transformers actual technical state, and using this information the operator can decide if any actions should be taken in the future. A detailed survey [1] has been conducted to analyze the causes of transformer failure in high voltage systems. The main failure modes across all voltage classes are dielectrical (36.6%), mechanical (20.0%), electrical (16.5%), and thermal (10.9%). The methods, which have recently been used to comprehensively assess transformer technical condition, are described in [2]. Lately, approaches havebeen made to unify transformer measurement data into a single health index. Some of them [3; 4] are already in use, but unfortunately they are not complex enough, as they mainly focus on dissolved gas analysis (DGA) and physical-chemical oil data. In a study including a mathematical Markovian model [5], authors attempt to find the optimum timespan between two specific inspections (DGA and FRA) in order to maximize availability and optimize maintenance costs. Frequency Response Analysis (FRA) is a test method used for assessment of mechanical condition of a transformer active parts. It is based on the measurement of winding response to a wide frequency sine signal. FRA is a comparative method, in which differences between two frequency response curves are analyzed, therefore it needs some \"fingerprint\" data measured in the transformer healthy state (the best option is right after installation). It is utilized as a diagnostic technique following such incidents as short circuits or lightning strikes. However, assessments using this method can provide critical information on a transformer winding state and may eventually lead to strategic decisions to remove the unit from further operation. At the current stage of FRA method development, it is possible to perform repetitive measurements. In 2012, an IEC standard on a measuring technology [6] was published, and most available commercial devices fulfill its requirements. The biggest problem of FRA method is interpretation of test results, namely the relationship between the scale of differences between curves and decision for further operation of a given transformer. Very often, visible differences between two FRA curves recorded for the same winding over time do not mean that there is a deformation in the winding. The cause of curve shift (resonance shift or damping change) may come from other elements of the transformer, e.g., different positions of the on-load tap changer (OLTC) or core magnetization caused by previous DC measurements, which influence inductance parameters. Similarly, some changes, like bushing replacement, may influence capacitive parameters [7; 8; 9; 10]. Usually in industrial measurements, results are recorded in one test configuration: end-to-end open. In such cases, only the winding of the measured voltage side is taken into consideration, with some capacitive influence of other windings.