Increased pressure on high voltage power distribution components has been created in recent years by a demand to lower costs and extend equipment lifetimes. This has led to a need for condition based maintenance, which requires a continuous knowledge of equipment health. Power transformers are a vital component in a power distribution network. However, there are currently no established techniques to accurately monitor and diagnose faults in real-time while the transformer is on-line. A major factor in the degradation of power transformer insulation is partial discharging. Left unattended, partial discharges (PDs) will eventually cause complete insulation failure. PDs generate a variety of signals, including electrical pulses that travel through the windings of the transformer to the terminals. A difficulty with detecting these pulses in an on-line environment is that they can be masked by external electrical interference. This thesis develops a method for identifying PD pulses and determining the number of PD sources while the transformer is on-line and subject to external interference. The partial discharge detection system (PDDS) acquires electrical signals with current and voltage transducers that are placed on the transformer bushings, making it unnecessary to disconnect or open the transformer. These signals are filtered to prevent aliasing and to attenuate the power frequency, and then digitised and analysed in Matlab, a numerical processing software package. Arbitrary narrowband interference is removed with an automated Fourier domain threshold filter. Internal PD pulses are separated from stochastic wideband pulse interference using directional coupling, which is a technique that simultaneously analyses the current and voltage signals from a bushing. To improve performance of this stage, the continuous wavelet transform is used to discriminate time and frequency information. This provides the additional advantage of preserving the waveshapes of the PD pulses for later analysis. PD pulses originating within the transformer have their waveshapes distorted when travelling though the windings. The differentiation of waveshape distortion of pulses from multiple physical sources is used as an input to a neural network to group pulses from the same source. This allows phase resolved PD analysis to be presented for each PD source, for instance, as phase/magnitude/count plots. The neural network requires no prior knowledge of the transformer or pulse waveshapes. The thesis begins with a review of current techniques and trends for power transformer monitoring and diagnosis. The description of transducers and filters is followed by an explanation of each of the signal processing steps. Two transformers were used to conduct testing of the PDDS. The first transformer was opened and modified so that internal PDs could be simulated by injecting artificial pulses. Two test scenarios were created and the performance of the PDDS was recorded. The PDDS identified and extracted a high rate of simulated PDs and correctly allocated the pulses into PD source groups. A second identically constructed transformer was energised and analysed for any natural PDs while external interference was present. It was found to have a significant natural PD source.