Real-time pricing considering carbon constraints for smart grid with multiple energy sources.

The article focuses on developing a real-time electricity pricing strategy for smart grids that integrates carbon emission costs and clean energy generation to maximize social welfare. It proposes a social welfare maximization model combining traditional fossil fuel power and clean energy sources, incorporating carbon emission costs via a weighted multi-objective optimization approach transformed into a single-objective problem. A distributed iterative algorithm based on the subgradient projection method is employed to solve the dual problem, enabling privacy-preserving, efficient computation of real-time prices and optimal power allocation. Numerical simulations demonstrate that including carbon emission costs in pricing reduces traditional energy supply, increases clean energy use, raises electricity prices to reflect environmental costs, and enhances overall social welfare, thereby promoting the low-carbon transition of the power sector.