Enhancing peer-to-peer energy trading in Integrated Energy Systems: Gamified engagement strategies and differentiable robust optimization

The transition to low-carbon energy systems requires innovative solutions to address renewable energy variability, demand-side uncertainty, and user engagement. Integrated Energy Systems (IES) link electricity, gas, and heat to improve grid flexibility and renewable integration. This paper presents a novel framework for optimizing community energy management in IES, incorporating behavioral insights, advanced optimization, and gamification. Using Self-Determination Theory (SDT) to model user motivations, the framework integrates a differentiable Distributionally Robust Optimization (DRO) layer for uncertainty handling in energy forecasting. Gamification strategies incentivize user participation, aligning individual behavior with system goals. A multi-objective model minimizes costs, enhances flexibility, and promotes sustainability. A case study demonstrates that the framework reduces system costs approximately by 15%, cuts carbon emissions nearly by 20%, and increases user engagement scores roughly by 25% compared to conventional strategies. This work contributes: (1) integrating SDT and DRO for energy management, (2) a DRO layer for robust machine learning, (3) a multi-objective optimization framework, and (4) gamification strategies to enhance user participation. The framework bridges technical and behavioral approaches, offering actionable insights for resilient energy systems.