Investment in source-grid-load-storage (SGLS) systems is distorted by market power: renewable, storage and demand-response (DR) agents withhold output and under-build flexibility. This paper formulates a two-level Stackelberg game in which a regulator sets a renewable premium σR (CNY/MWh) and a peak flexibility payment σF (CNY/kW·yr) settled on net peakwindow injection, while three agents play a Nash equilibrium under an endogenous merit-order price and internalize their own price impact. Storage carries SOC dynamics, power limits and a cyclic condition; net-injection settlement removes any reward for charge-discharge churn. The social cost is a resource cost, so premia and tariffs enter as transfers. A Shapley value allocates the cooperative surplus. On a synthetic 80 MW example, the unregulated equilibrium sits 28.9% above the planner's optimum; a price-taking benchmark attributes 26.6 points to market power and 2.3 to unpriced peak/ramping externalities. The instruments (450,400) close 91.7% of the gap, cut annual CO2 from 3.25×105 to 1.13×105 t and the peak from 62.6 to 35.8 MW. One policy applied to four scenarios forfeits 0.22% against clairvoyant per-scenario policies. Under a common budget cap the pair beats the premium alone (83.3%), the flexibility payment alone (11.4%) and all twelve declining-block designs (best 81.0%); a revenue-neutral TOU tariff closes 0.1% and is not used when offered as a third instrument. The Shapley allocation (90.8/5.4/3.8%) lies in the core.
Jie Teng, Chang Liu, Luo Huang et al.· 2026 5th International Confe...· 0 citations
The rapid expansion of distribution networks and the increasing complexity of their topological structures pose significant challenges to fast and reliable post-fault service restoration. Meanwhile, driven by carbon neutrality goals, the large-scale integration of distributed energy resources (DERs) enhances operational flexibility but also introduces pronounced intermittency and uncertainty, further complicating post-fault load transfer decision-making. To address these challenges, this paper proposes an expert-guided and virtual power plant (VPP)-assisted load transfer optimization framework based on hierarchical graph reinforcement learning. A topology-aware graph neural network (GNN)–based state representation is developed, in which buses are modeled as nodes and switches as controllable edges, enabling explicit modeling of network connectivity and electrical coupling. On this basis, a hierarchical decision-making architecture is constructed: the upper-level agent, guided by expert knowledge, dynamically selects the restoration task type to coordinate the timing of network reconfiguration and VPP-assisted DER regulation; driven by this high-level directive, two specialized lower-level agents respectively execute the specific switch operations and stepwise DER power adjustments, ensuring power balance and voltage security. Simulation results on a practical distribution network demonstrate that, under high DER penetration, the proposed method achieves faster service restoration, higher load recovery ratios, and significantly fewer voltage violation events than conventional reinforcement learning approaches, exhibiting improved operational safety and scheduling stability.
Lu Chen, Jinhu Fang, Xiaona Lv et al.· PLoS ONE· 0 citations
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