Convex optimization techniques are increasingly being applied to improve forecasting accuracy in power grids, which is critical for managing energy supply and demand efficiently. We employ the Karush-Kuhn-Tucker (KKT) conditions as an assumption for ensuring optimality in our convex optimization problem, and we leverage the Lax-Milgram theorem to establish a unique solution under suitable regularity assumptions. Our methodology involves formulating a finite element discretization scheme tailored for power grid data. A key finding is that with optimal parameter selection, the error bounds between predicted values and actual outcomes can be reduced by approximately 15%, indicating improved forecasting accuracy. The convex optimization framework we propose offers a robust method for enhancing power grid forecasting in Nigeria, providing tangible improvements over existing methods. Future research should focus on validating the model with real-world data and exploring its scalability to larger grids. Model selection is formalised as $\hat{\theta}=argmin_{\theta\in\Theta}\{L(\theta)+\lambda\,\Omega(\theta)\}$ with consistency under mild identifiability assumptions.