TITLE:
Optimization Method for Distribution Locational Marginal Pricing Considering Stepped Carbon Trading and Source-Grid-Load-Storage Coordination
AUTHORS:
Haolong Wu
KEYWORDS:
Social Welfare Maximization, Distribution Locational Marginal Pricing (DLMP), Stepped Carbon Trading, Electric Vehicles (EVs), Second-Order Cone Programming (SOCP)
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.3,
March
19,
2026
ABSTRACT: The high penetration of distributed energy resources (DERs) exacerbates net load fluctuations in distribution networks. Existing dynamic pricing research often ignores complex physical constraints, yielding dispatch outcomes that are “mathematically optimal yet physically infeasible”. To address this, we propose a day-ahead optimal dispatch and pricing strategy that jointly considers AC power flow constraints and a stepped carbon trading mechanism. We establish a market framework—integrating distributed generation, energy storage, and electric vehicle aggregators—to reinforce low-carbon incentives. A continuous second-order cone programming (SOCP) relaxation is employed to address power flow non-convexity, ensuring strict adherence to voltage and line security limits. Based on duality theory, the Distribution Locational Marginal Price (DLMP) is analytically derived to comprehensively internalize the spatial-temporal marginal costs of energy, congestion, losses, and carbon emissions. Simulations on a modified IEEE 33-bus system demonstrate that these spatiotemporally differentiated price signals effectively guide flexible resources to mitigate voltage and congestion risks. Compared to traditional fixed pricing, the proposed DLMP mechanism maximizes social welfare by unlocking higher user utility and rationally internalizing environmental costs, validating its effectiveness in fostering the low-carbon synergistic optimization of “Source-Grid-Load-Storage”.