Abstract:
Energy, as both a direct and indirect fundamental life-supporting resource, has
experienced a steady rise in domestic and industrial demand, driven by technological
advancement, population growth, and economic expansion. Various sources of energy
including fossil fuels, hydroelectric power, geothermal energy, wind, solar, and
nuclear are available in different proportions, each with distinct cost structures and
environmental impacts. The challenge of meeting these diverse needs while
minimizing production and distribution costs, conserving the environment, and
reducing wastage has evolved into a complex multi-objective problem. This research
focuses on the mathematical modelling of the optimal energy mix and the
optimization of renewable resources, with particular emphasis on individualized
demand profiles. The objectives are threefold: first, to formulate a mathematical
model for analysing the dynamics of energy demand, production, and distribution;
second, to determine the parameter thresholds that guarantee stability and robustness
of the optimal energy mix; and third, to develop a smart grid feedback model using
adaptive neural networks capable of automatically maintaining the desired energy
balance. The methodology entails formulating a system of differential equations to
represent the energy system, expressing it in state-space form, and applying Laplace
transforms to derive transfer functions. These will be analysed for sensitivity,
stability, and robustness using Nyquist and Bode plot criteria. MATLAB–Simulink,
equipped with neural network modules, will then be employed to simulate and
implement an intelligent, adaptive feedback control system. Through these
simulations, the study will integrate real-time learning and self-adjustment capabilities
to align production with demand in the most efficient manner. The anticipated
outcome is an automated, smart distribution system capable of dynamically meeting
individualized energy requirements at the lowest possible cost, while enhancing the
utilization of renewable sources and reducing reliance on non-renewable options.
Ultimately, this approach aims to promote environmental sustainability through
increased adoption of green energy technologies.
