The growing rate of urbanisation and the ever-increasing electrification of urban homes, industries, and businesses still pose a significant burden on urban distribution systems, creating frequent peak-load demands, voltage fluctuations, and unnecessary energy waste. In this regard, the present paper proposes a comprehensive theoretical and mathematical framework for a Smart Energy Management System (SEMS) engineered to enhance real‑time energy utilisation efficiency in such intricate settings. The proposed SEMS incorporates a multi‑layer analytical architecture that integrates IoT‑inspired sensing, edge‑level preprocessing, cloud‑based data structuring, and AI‑driven predictive modelling, thereby enabling the accurate capture and analysis of electrical behaviour with high temporal precision. To calculate the short-term power, cumulative energy consumption, and the changes in dynamic loads directly using voltage-current time-series information and a specific forecasting module, predict the imminent peak-demand durations to enable advance control. In addition to it, a multi-level optimisation mechanism is proposed to reschedule or curtail non-critical loads in the predicted overload cases with analytical expressions estimating the achievable saving of the energy by the demands shifting. The theoretical results show that the SEMS can, in the realistic context, achieve the reduction of peak-hour demands by 12 -18% and the improvement of grid stability and consumer engagement without requiring significant hardware changes or expensive infrastructural improvements. In general, the work has shown that mathematically based SEMS architectures provide a scalable, economical, and practically deployable avenue towards the modernisation of urban energy management, especially in resource-limited developing areas, and has provided a strong platform on which the future empirical validation and practical implementation can be realised.