High voltage power transformers are designed to withstand a variety of overvoltages and short circuit forces. Occurrence of these events in a power system is natural, inevitable, and one of the main causes of transformer failure. Therefore, an early and reliable detection of an incipient fault is paramount. To this end, diagnostic testing and condition monitoring, not only enables power utilities in early detection of incipient fault-like conditions, but also is a practical way of optimizing existing assets, lowering operating costs, scheduling maintenance, preventing unplanned outages, etc. and consequently improve efficiency. Over the years, many monitoring and diagnostic methods have evolved. In par- ticular, low voltage impulse and frequency response analysis or transfer function approaches have emerged as useful tools in detecting winding deformations. Literature study reveals that although much has been acclaimed about these methods, advancement in interpretation of acquired data must be rigorously pursued, to facilitate a more meaningful assessment. As a matter of fact, diagnosis (which means interpretation of monitored data) has at-the-most been confined to a mere comparison of two subsequently acquired data sets. This philosophy certainly needs to be improved, to realize the true potential of monitoring/diagnostic tools. Achieving this goal calls for newer impetus. It is natural that there will arise many problems while achieving this goal and they will have to be resolved. Keeping these aspects in mind, the objective of this thesis was aimed at developing Solutions to two specific topics that are closely related to and concern the transformer winding, namely, * An efficient solution to the generalized model of a transformer winding, with no particular limitation on the size of network and number of windings, no restriction on circuit topology and terminal condition, etc. * Propose a method to locate the position, quantum and type of change (i.e. deformation) a model winding undergoes, based on terminal measurements. Details of these approaches are presented in this thesis, which is divided into two parts. 1. A comprehensive analysis of the behaviour of a transformer winding under impulse excitation and its interaction with adjacent windings was until now severely limited, due to the simplifying assumptions imposed (by the existing approaches), like neglecting interaction with neighbouring windings, Ignoring loss, considering only a few sections, etc. thereby rendering the computed results less accurate. A solution considering all these aspects often times results in a very large-sized circuit that needs to be solved. Although circuit simulation software afford iterative solutions, a direct estimation of poles and zeros of any desired network function is not possible. In the first part of the thesis, a novel and closed-form (i.e. analytical) solution based on state space analysis is proposed. It is shown, how the renders the entire computation to be purely numeric. Thus, time-consuming symbolic manipulations are avoided. With this feature, there is practically no limit on the size of network and no restriction on circuit topologies that can be considered. So, virtually any number of windings of a transformer can be considered, permitting a comprehensive analysis of winding behaviour and its interactions. Further, the formulation also permits computation of poles and zeros of any desired network function (e.g. transfer admittance), response to any excitation (e.g. neutral current, transferred surge), estimation of voltage distribution, etc. with little extra effort. Hence, it would be apppropriate to term the proposed method as a \Generalized" solution. For the sole purpose of demonstration, a large-sized network (representing a two-winding transformer with 250 sections/winding) was solved and required only 700 seconds. This shows the time-efficiency achieved, and also that it is free from issues like numerical instability, convergence problems, etc. encountered in some of the existing methods. 2. Detection of mechanical deformation in transformer windings can be achieved with a fair degree of sensitivity using frequency response methods. However, a major challenge that has remained elusive is ascertaining the \extent of damage" and likewise \its location along the winding". It is needless to say that finding these answers is crucial. Ideally, a diagnosis tool is expected to be endowed with powers to answer these questions. Therefore, it is desirable to explore alternative ways of harnessing these embedded features, if any. This was the next motivation. Obviously, a direct solution to this problem on an actual transformer winding is far too complex. Hence, in this preliminary effort a solution was attempted considering a model winding. However, care was taken to incorporate other winding-related nuances as far as practicable. The method was formulated based on quantities measured at the terminals. In the second part of the thesis, a novel algorithm is proposed for determining the location, extent and type of changes intrroduced in a model winding, based on terminal measurements. It employs the well-known properties of driving-point functions and adopts an iterative circuit synthesis approach. From knowledge of the measured short-circuit and open-circuit natural frequencies, and some relevant winding design data, an equivalent circuit was synthesized (called reference circuit). Next, changes were introduced at different locations in the model winding and natural frequencies measured again. Corresponding to every new set of measured natural frequencies, a fresh circuit was synthesized (with topology remaining unchanged). A comparison of these circuits with the reference circuit revealed that a mapping could be established between changes introduced in the model winding and those predicted by the synthesized circuits. Initially, the underlying principle is discussed, and thereafter, the experimental results are presented for both continuous-disc and interleaved winding representations. The case studies involved examples wherein changes in the model winding were made to elements connected to a single tap, two physically different tap positions, multiple changes to different elements, and so on. In all cases, the positions of all the `changes' were reasonably well locatable, and so was the `type of change'. The results were very encouraging. In summary, localization of changes based on terminal measurements, is shown to be a possibility. Lastly, it is conjectured that these findings could be of some assistance in addressing the ultimate task of locating mechanical deformations in actual transformer windings.