Mathematical modeling of resilient and sustainable renewable energy integration with hybrid energy storage, emission constraints, and extreme weather conditions

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The transition to sustainable energy is vital to curb emissions while meeting rising demand. Yet solar, wind, and hydropower are variable and stochastic, complicating reliable grid integration. This study asks a central question: how can hybrid energy storage be optimally integrated with renewables under extreme weather to improve resilience, efficiency, and sustainability? This study develop a comprehensive mathematical framework that co-optimizes battery, hydrogen, and thermal energy storage using advanced stochastic methods. Uncertainty in renewable availability, weather shocks, and demand surges is modeled with probabilistic resilience metrics derived from Generalized Extreme Value and Generalized Pareto distributions, enabling risk-aware dispatch. The framework also enforces carbon-emission limits and renewable-penetration targets aligned with current sustainability policies and market constraints. A rural-India case study evaluates performance across stress scenarios. Results show improved resource allocation, higher reliability, lower curtailment, and credible pathways toward carbon-neutral operation even during rare, high-impact events. Overall, the approach delivers robust operations under high renewable variability and provides actionable guidance for policymakers, utilities, and planners designing resilient, efficient, low-carbon power systems. Implementation details include scenario-based optimization, chance constraints for reliability, and multi-period dispatch scheduling, ensuring practical applicability and scalability for diverse geographies and grid conditions.

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