Frequency response analysis (FRA) of transformers is universally accepted as a highly sensitive tool to detect deformations in its windings. This is evident from the fact that customized commercial equipment (popularly called FRA or SFRA instruments) are used and recently the IEEE has issued a draft trial-use guide. Nevertheless, use of FRA is still limited to only detection and there is little progress towards its use for localization of winding deformation. Toward this end, a possible approach would be to compare the healthy and deformed systems in a suitable domain, e.g., their respective models could be compared. In this context, the mutually-coupled ladder network is ideally suited because not only does it map the length of the winding to sections of the ladder network, but, also inherently captures all subtle intricacies of winding behaviour under lightning impulse excitations insofar as the terminal response, internal oscillations and voltage distributions are concerned. The task of constructing a ladder network from frequency response is not trivial, and so exploration of newer methods is imperative. A system can comprehensively be characterized by its frequency response. With this as the starting point, many approaches exist to construct the corresponding rational function (in s-domain). But, the subsequent step of converting this rational function into a physically-realizable mutually-coupled ladder network has, as yet, remained elusive. A critical analysis of the circuit synthesis literature reveals that there exists no analytical procedure to achieve this task, a fact unequivocally stated by Guillemin in his seminal book "Synthesis of Passive Networks". In recent years, use of iterative methods to synthesize such ladder networks has also been attempted with some degree of success. However, there exists a lot of scope for improvement. Based on this summary, the objectives of this thesis are as follows- _ Development of an analytical procedure, if possible, to synthesize a mutually-coupled ladder network starting from the s-domain representation of the frequency response _ Construction of a nearly-unique, mutually-coupled ladder network employing constrained optimization technique and using frequency response as input, with time-efficiency, physical realizability and repeatability as its features In Chapter 2, analytical solution is presented to convert a given driving-point impedance function (in s-domain) into a physically-realizable ladder network with inductive couplings (between any two sections) and losses considered. The number of sections in the ladder network can vary, but, its topology is assumed fixed. A study of the coefficients of the numerator and denominator polynomials of the driving-point impedance function of the ladder network, for increasing number of sections, led to the identification of certain coefficients, which exhibit very special properties. Generalized expressions for these specific coefficients have also been derived. Exploiting their properties, it is demonstrated that the synthesis method essentially turns out to be an exercise of solving a set of linear, simultaneous, algebraic equations, whose solution directly yields the ladder network elements. The proposed solution is novel, simple, and guarantees a unique network. Presently, the formulation can synthesize a unique ladder network up to 6-sections. Although it is an analytical solution, there are issues which prevent its implementation with actual FRA data. Keeping the above aspect in mind, the second part of the thesis presents results of employing an artificial bee colony search algorithm for synthesizing a mutuallycoupled lumped-parameter ladder network representation of a transformer winding, starting from its measured magnitude frequency response. The bee colony algorithm is modified by defining constraints and bounds to restrict the search-space and thus ensure synthesis of a nearly-unique ladder network, corresponding to each frequency response. Ensuring near-uniqueness while constructing the reference circuit (i.e., a uniform healthy winding) is the objective. The proposed method is easy to implement, time-efficient, ensures physical realizability and problem associated with supply of initial guess in existing methods is circumvented. Experiments were performed on two types of actual, single, isolated transformer windings (continuous-disc and interleaveddisc) and the results are encouraging. Further details are presented in the thesis.

Frequency response analysis (FRA) has emerged as the de-facto industry standard condition-monitoring tool to assess mechanical integrity of transformer windings during its service life. It the prerequisite detection sensitivity and customized portable commercial instruments are also available. Considering its importance and taking cognizance of its hidden potential, international bodies, viz., IEEE, IEC, and CIGRE have published standards/guides on its use and interpretation. In spite of all the progress witnessed over the past two decades, FRA has still not attained the status of a diagnostics tool. Probing the vast literature and research carried out in this points to the fact that lack of a rigorous mathematical basis to explain the underlying complex processes is, perhaps, one of the main reasons for the present predicament of FRA method. How-ever, it must be acknowledged that domain-knowledge is di cult to generalize in this. Having said that, the diagnostic part, which involves, the task of working back-wards starting from the FRA data to interpret a winding damage, locate it, and assess its severity, has so far remained teasingly elusive. As a consequence, FRA continues to remain as a sensitive condition-monitoring tool. Given its inherent potential, this situation seems to be a paradox, and so, calls for investigations. Once a mechanical damage has been detected by FRA, the next task is to locate its position and estimate its severity. An engineer expects FRA to provide these answers, so that corrective action, if needed, can be determined and initiated. In this context, even though FRA has attained global acceptance as a monitoring tool, it has failed as a diagnostic tool. Therefore, e orts that aim to address this issue are desirable. Driven by this motivation, the author's thesis proposes to explore a new school of thought in this direction, viz., to theoretically analyze the problem of localization of an incipient/minor mechanical damage (displacement in particular) and also assess its severity. Such an investigation seems to have not been undertaken previously. So, the goal is to establish a relationship to capture the complex interactions that exist between specific winding damages, winding parameters, and their overall in hence on the natural frequency deviations observable in the FRA data. Hence, exploring this possibility, subject to the constraint that the proposed method shall use inputs that are measurable at the terminals, becomes the primary objective of this research. In this thesis, a generalized analytical framework for handling winding displacements and FRA data has been successfully formulated. The formulation provides a general platform for localization and severity assessment of true radial and axial winding dis-placements occurring in an actual winding. An analytical solution becomes possible mainly due to manipulation of the system matrix, i.e., to consider the harmonic sum of squares of natural frequencies, instead of just the natural frequencies. This manipulation leads to an elegant closed-form expression that connects the displacement location and its severity, to changes in natural frequencies. For its implementation, short circuit natural frequencies and a few other terminal measurements are the only inputs that are necessary. This formulation is initially used in Chapter-3 to demonstrate localization of radial displacement in an isolated, actual, single, air-cored continuous-disk winding. Armed with this success, the supplicant proceeds further to show (in Chapter-4) how a minor manipulation of the formulation renders it suitable for localization of actual axial displacements as well. Extensive experimental verification was done and the results are encouraging. Accuracy of localization of radial/axial displacement is uniformly good for all positions, and so is the estimation of severity. Further details are presented in the thesis.