The factory acceptance tests are extremely important for the deployment and service life of Extra-high voltage transformers (EHV) and reactors. An essential part of such tests is Lightning Impulse (LI) tests which are intended to ensure that the transformer insulation withstands the transient lightning overvoltages which may occur while in service. These tests are usually done with negative polarity to prevent air side flashovers. In recent years, there has been an increasing demand for additional positive polarity lightning impulse tests to secure the reliability and life of the transformers. The transformer, during its service life, is subjected to massive electrical stresses due to lightning strikes and switching impulses. As a consequence, this may lead to the degradation of the transformer insulation. During lightning impulse tests, ionisations might occur in the pressboard/insulating liquid insulation system, which would lead to the development of space charges. The space charges generated may have an influence on the withstand behaviour of the insulation corresponding to applied impulse voltage. There is also a possibility of field enhancements due to the effect of space charge, especially when tested consecutively with opposite polarity. During the acceptance tests on transformers at SGB-SMIT transformers, a waiting period of one hour is given between the negative polarity LI and positive polarity LI. This arbitrary waiting time is given under the assumption that this will allow any ’trapped’ charges to decay and provide relaxation time for the slower polarisation processes. So the main question is whether this waiting period allows sufficient time for the decay of charges in the transformer insulation. For this analysis, the relaxation time characteristics of the transformer insulation system were investigated by estimation of the time dependency of depolarisation currents in the oil, paper/pressboard insulation. In this thesis, the characteristic of the time-domain dielectric response and the time dependency of the currents due to depolarisation of charges under DC and impulse voltage was investigated by the polarisation-depolarisation current (PDC) measurements on the test samples. The PDC method is a non-destructive diagnostic method for evaluating transformer insulation in the time domain. A test set up was built to represent a simplified model of transformer insulation comprising of mineral oil, paper and pressboard. The measurements of discharge voltage over time were conducted on the test samples of oil, paper and pressboard to understand the time-dependency of polarisation-depolarisation processes occurring within the transformer insulation. Two dominant time constants of decay were estimated for oil, paper and pressboard samples. The results from the discharge voltage measurement were compared with the analytical solution of the output voltage of the equivalent R-C circuit of the test sample which revealed that there were more than two polarisation phenomena occurring within the composite test sample of oil, paper and pressboard. Later, to mitigate the inconsistencies with the simplified R-C model, it was extended and modified based on the linear dielectric response theory to study the dielectric response behaviour of transformer insulation under DC voltage for longer charging times (tc=10,000 seconds). The modified R-C model was envisioned and developed in PSPICE simulation environment. The model incorporates the effect of the individual polarisation processes occurring within the constituent dielectrics of transformer oil-paper-pressboard insulation. The dielectric properties like conductivity and dielectric response function f (t ) can be estimated reasonably accurately with this modified R-C model. A comparison of the maximum and minimum values of the polarisation currents of the composite test sample obtained from the simulated model and from dielectric testing was conducted. The results demonstrated that relative errors were limited to a maximum of 8 %. The time-domain polarisation and depolarisation behaviour of composite transformer insulation was analysed under DC and impulse voltages from simulations of PDC measurements using PSPICE simulation software. It was observed that for the same thickness of solid insulation, as the oil-gap increases, the magnitude of the depolarisation current at the end of the discharging period (10,000 seconds) also increases. For identical oil-gaps, as the thickness of the pressboard in the composite test sample of oil-paper-pressboard was increased, the depolarisation currents show a delayed response to decay to a minimum value at the end of discharging duration. The time dependency of depolarisation currents at the end of discharging time of one hour was realised for impulse voltages. The study of the depolarisation currents under the influence of impulse voltage revealed that the charge induced field at the end of the discharging period of one hour does not exceed the permissible threshold electric field of 2 kV/mm inside the transformer insulation. In the future, the model could be developed into a valuable diagnostic tool for studying the dielectric responses of complex transformer insulation under the influence of different parameters like moisture content, ageing products, geometrical configuration and temperature.