The present Low Voltage (LV) grid, which until recently was mainly composed of passive electrical components (consumers), is being gradually overrun by active electrical components (prosumers), who not only consume but also generate and share power locally. This development is introducing changes in the operational dynamics of the LV grid that could result in voltage stability problems and the violation of infrastructural constraints if not well managed. A re-design of the present LV grid is, therefore, imperative to enable it meet these new requirements. This thesis was aimed at studying the influence of topological metrics on the operational performance of the LV grid in view of current developments in energy consumer behaviour with a view to proposing the topological changes and/or modifications in network architecture that would yield optimal outcomes. We modelled the present LV grid as a radial network, and compared it to three other network models -random, small-world and scale-free networks- under different loading scenarios. We proposed novel structural and operational metrics that are suitable for the LV grid, and analysed the networks in terms of these metrics. We also compared their robustness under different attack scenarios and demonstrated the correlation between the structural and the operational metrics, thus, identifying important structural metrics that need to be optimized to improve the future LV grid performance. Finally, we then investigated the possible modifications of the radial network model of the present LV grid that would yield similar results. The results highlighted the structural weaknesses of the present LV grid under futuristic and simultaneous loading conditions and presented the scale-free model as the most suitable architecture for the future LV grid as it out-performed all the other network models under similar loading conditions. They also showed that the insertion of additional links at critical positions in the radial network could achieve similar results. We therefore proposed this structural modification as a more cost-effective approach to improved operational performance of the LV grid.