Two-layer iterative optimization for enhanced electricity–carbon pricing to promote renewable integration and load smoothing with multi-type prosumer

The increasing penetration of photovoltaic (PV) prosumers in distribution systems has exacerbated the peak-to-valley load gap, leading to imbalances between electricity supply and demand. To address this challenge, this paper proposes a two-layer iterative optimization-based enhanced electricity–carbon pricing approach, designed to incentivize users to smooth load curves and enhance renewable energy accommodation. In the upper layer, the distribution system operator designs customized time-of-use, reactive power, demand, on-grid, and carbon prices for PV prosumers and consumers, aiming to minimize power purchase, carbon trading, and network loss costs while adhering to power flow constraints. In the lower layer, users respond to these price signals by configuring energy storage and optimizing operational strategies, considering PV uncertainty to minimize power transaction, carbon trading, and energy storage configuration costs. Simulation results based on a modified IEEE 15-bus distribution network show that the proposed approach achieves a 13.44% improvement in social welfare, a 27.8 kW reduction in the peak–valley load difference, and a 120 kg decrease in carbon dioxide emissions, highlighting its effectiveness in enhancing both economic and environmental performance.