Developing Fundamental Understanding of Transformer Frequency Response through White-box and Genetic Algorithm based Grey-box Models

Abstract

Power transformer is one crucial component in the modern power grid. Ensuring the safety operation and reliability of power transformers is of great importance. Transformer winding mechanical fault is one of the major contributors to transformer failures. Frequency Response Analysis (FRA) has been found as the most sensitive and effective technique for detecting winding mechanical faults. However, the challenge of FRA application lies in the correct interpretation of FRA traces, and a good knowledge of transformer structures and their consequential impacts on FRA traces is required. Numerous sensitivity studies, either by experimental or simulation methods, have been conducted to investigate how different winding parameters affect the corresponding FRA characteristics. This PhD thesis focuses on the mathematical theory linking the transformer winding equivalent electrical components with the main FRA features. Three FRA characteristics in the low frequency region, i.e. ‘U’, ‘V’ and ‘∩’ shape curves, have been observed in IEC 60076-18 and CIGRE FRA Technical Brochure 342, while the physics behind them remain unexplained. This PhD research uses a white-box modelling technique to build up single winding model and a base single-phase two-winding transformer model, and the mathematical expression representing the three low frequency FRA features is derived by applying Basic Circuit Theory and Electric Potential Energy Conservation on the corresponding transformer models. It is found that winding space coefficient α, which is constituted by winding series and ground capacitances, is the key to determine the low frequency FRA features of single winding, while for a single-phase two-winding transformer, the equivalent winding capacitances seen from tested terminals contribute to an equivalent space coefficient αr. In the high frequency region, the mathematical expressions representing different FRA patterns at high frequencies are derived by applying Transmission Line Theory on single winding model, and it is concluded that winding space coefficient α remains its dominant status on determining different FRA patterns. These findings enhance the fundamental understanding of FRA and contribute to the identification of key parameters on FRA fingerprints. In practice, the complete set of transformer geometric parameters is often not available, which constrains the FRA interpretation work through white-box modelling. A grey-box modelling technique, which only utilises limited measurement information such as FRA, winding resistance, capacitance and power factor tests results, is developed to provide a simulation tool for FRA interpretation. With the knowledge obtained from white-box modelling technique, the individual parameter of electrical component in the transformer equivalent circuit is calculated according to winding geometric design, and Genetic Algorithm (GA) is used to optimise the unknown values of electrical components. In the optimisation procedure, the Complex Distance (CD), calculated by FRA reference and simulation results, serves as the fitness to assess the optimisation accuracy. The termination condition is set in a way of the compromise between accuracy and time consumption. The validity of the method is demonstrated by case studies of two single windings with different types and the base single-phase two-winding transformer. Such a grey-box modelling approach provides an alternative for FRA interpretation when white-box modelling technique is constrained. This PhD study has further advanced the fundamental understanding of typical characteristics observed on transformer FRA measurement results, and developed a Genetic Algorithm based grey-box modelling technique as an alternative to white-box modelling. It is envisaged that such a simulation tool can be then used to produce a FRA fingerprint library of different types of winding mechanical faults at different locations, for FRA interpretation.

Date of Award	1 Jan 1824
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Zhongdong Wang (Supervisor)