A spatiotemporal causal inference based multi-level game framework for load balancing among fast charging stations

—The rapid growth of electric vehicles (EVs) intensifies spatiotemporal charging load imbalances among fast charging stations (FCSs). Temporally, intra-station peak-valley gaps cause short-term power distribution network (PDN) overloads, while spatially, inter-station load imbalances lead to significant resource utilization disparities. To address these challenges, this paper proposes a spatiotemporal causal inference based multi-level game framework for load balancing among FCSs, which coordinates interactions between PDN, FCSs, and EVs for load balancing. Considering the heterogeneity of inter-station relationships, a spatiotemporal correlation analysis method based on causal inference is developed that employs dynamic causal mixture models to distinguish genuine relationships from spurious correlations. The method integrates spatiotemporal correlation analysis with functional causal effect evaluation and constructs a causal-enhanced relevance network, quantifying directional influences while improving both analytical precision and interpretability of FCS interactions. Building on the correlation of FCSs, a multi-level game framework is designed, proposing hierarchical incentive transmission with inter-station equitable cost-allocation mechanisms, guiding spatiotemporal transfer of charging demand through coordinated pricing strategies, and optimizing load distribution across the FCSs. To efficiently solve the resulting complex optimization problem, an improved alternating direction method of multipliers (ADMM) algorithm is implemented with dynamic relaxation factors that adapt to gradient direction and residual information, enhancing convergence performance and solution stability. Case studies using real-world transportation and PDN validate the effectiveness of the proposed approach, achieving substantial load imbalance reduction while enhancing voltage stability and charging facility utilization across the integrated system.