Energy management in a grid-connected microgrid using hybrid Golden Jackal optimization and gradient descent optimization and the concept of loadability

• Combines Golden Jackal Optimization and Gradient Descent for energy management. • Hybrid algorithm enhances convergence speed and robustness in microgrid operations. • Addresses loadability concept for stable microgrid performance under varying conditions. • Utilizes GJO for initial solutions; GD refines them for effective local convergence. • Demonstrates improved efficiency and reliability over standalone optimization methods. Golden Jackal optimization (GJO) maintains diversity and can simultaneously explore multiple regions of the search space since it operates on a population of solutions. However, the GJO has the demerit of deprived exploitation capability and it struck in local optima easily. For enhanced optimization efficacy, the suggested approach integrates a hybrid optimization algorithm that combines gradient descent and the GJO algorithm. The goal of this hybrid strategy is to influence the complimentary advantages of both algorithms: the local exploitation potential of gradient descent and the global exploration capabilities of GJO. The suggested hybrid method uses GJO to initialize a population of possible results. Then, iteratively exploring the search space, it notifies solutions based on GJO's mechanisms for exploration and exploitation. Furthermore, a portion of the population undergoes refinement using gradient descent in order to effectively converge towards local minima by utilizing local knowledge. The hybrid algorithm demonstrates improved convergence speed, robustness to diverse search space characteristics, and effectiveness in handling large-scale optimization problems compared to various optimization techniques including particle swarm optimization, pelican optimization, artificial bee colony, whale optimization algorithm and grey wolf optimization, standalone GJO and gradient descent algorithms. The total cost of the MG with the proposed methodology has reduced to 12017 rupees from 12350 by gradient descent and 12332 using GJO. Detailed comparison of various optimization techniques has been presented in the results section. Further, this paper also addressed the concept of loadability, which refers to the MG's ability to meet electricity demand under varying conditions, relying solely on its internal resources. Achieving optimal loadability in isolated MGs involves diversifying generation sources, leveraging energy storage systems, implementing demand-side management measures, utilizing predictive analytics, and designing resilient grid infrastructure. By implementing Bayesian sparse polynomial chaos expansion, the concept of loadability has been assessed. Due to which the MG operators can enhance energy management capabilities and maximize loadability, ensuring reliable and sustainable electricity supply to connected loads.