Optimizing renewable energy integration using advanced mathematical modeling with storage and emission constraints for resilient and sustainable energy systems

This study presents a stochastic optimization framework for the integration of renewable energy sources into modern power systems, aiming to address key challenges associated with variability in generation, demand uncertainty, and environmental constraints. The model simultaneously incorporates renewable and non-renewable generation, energy storage dynamics, and probabilistic resilience metrics to ensure system reliability, economic efficiency, and emission compliance. It employs a set of coupled energy balance equations, emission constraints, curtailment control strategies, and stochastic demand-supply interactions modeled via Beta and normal distributions. Applied to a rural Indian energy scenario, the model demonstrates a significant improvement over conventional configurations. Specifically, the optimized case with both storage and emission constraints yields a cost reduction of approximately 26%, a curtailment decrease of over 60%, and improved system resilience and reliability levels approaching 98%. These improvements validate the model's effectiveness in mitigating renewable intermittency, reducing operational inefficiencies, and supporting decarbonization targets. Socially, the model contributes to enhancing energy access and stability in underserved regions by optimizing resource allocation under real-world uncertainties. Practically, the framework provides a scalable and adaptable tool for policymakers, planners, and utility operators seeking to develop low-carbon, costeffective, and resilient energy infrastructures. By bridging theoretical modeling with practical system design, the proposed approach offers a valuable decision-support mechanism for transitioning to sustainable energy systems aligned with global climate commitments.