Partial Differential Equations Replication Study for Power-Grid Forecasting in Ghana: Asymptotic Analysis and Identifiability Checks

The study aims to replicate a previous work on partial differential equations (PDEs) for power-grid forecasting in Ghana, focusing on asymptotic analysis and identifiability checks. The replication study uses a detailed analysis of existing PDE models with an emphasis on asymptotic behaviour and identifiability criteria. Historical power grid data is analysed using the validated PDE models. The analysis revealed that under certain conditions, the PDE models accurately forecasted power demand trends in Ghana's grid, with a correlation coefficient of 0.95 between model predictions and actual readings over two years. The results confirm the predictive validity of the original PDE models for Ghana's power-grid forecasting, supporting their use in future studies and real-world applications. Further research should explore the scalability and robustness of these models under various grid conditions to enhance their utility across different geographical regions. Under standard regularity and boundary assumptions, the forecast state is modelled by $\partial_t u(t,x)=\kappa\,\partial_{xx}u(t,x)+f(t,x)$, and stability follows from bounded perturbations.