The development in electronics technology in the last decade has greatly increased the use of power electronic-based non-linear loads. This power electronic equipment consists of power electronic loads, Renewable Energy Sources (RES) (wind, solar PV etc.) and new technologies such as heat-pumps, Electric Vehicles (EVs) and LED lightings. Their greatest harmonic impact is expected on Low-Voltage (LV) distribution networks. For this reason, it is essential to develop a robust analytical tool for the analysis of the performance of LV networks in the presence of non-linear power electronic equipment.

In this thesis, a modelling framework is developed to enable a more accurate representation of the distribution system. The tensor, commonly used in physics to characterize the invariant relationship of vectors in the coordinate axis, is a way to achieve this phase-dependency representation accurately. PSCAD/EMTDC is a time-domain analysis tool, which inherently models this phase-dependency; however, it is incapable of modelling a complete distribution system. For this reason, it is used as a benchmark for MATLAB program development in the frequency-domain. Frequency-domain approach using tensor analysis has the ability to model very large electrical networks accurately.

This work proposed and implemented two optimisation methods: Fourier Descriptors (FDs) and Average Admittance Locus (AAL) for the approximation of tensors. The region of linearity of non-linear devices around the operating point of the device is determined. Laboratory experiment was carried out for the validation of tensors.

A test feeder is modelled to compare the accuracy of tensor analysis against the harmonic Current Injection (CI) method and also through time-domain PSCAD/EMTDC simulations. This validation leads to the implementation of tensor analysis on different LV distribution systems, city and urban network. Different loading scenarios are investigated due to the inherent fluctuating nature of residential and commercial loads. The results of tensor analysis are compared against the CI approach. The results show the greater accuracy of tensor analysis over the fixed CI method particularly as the voltage distortion increases. The harmonic CI method does not consider the harmonic interaction between non-linear devices and the a.c. system nor the interaction between multiple non-linear devices. Therefore, frequency-domain tensor analysis is expected to replace the CI method and time-domain methods for accurate harmonic studies of large electrical networks. E