The growing flexibility of load dispatching in modern smart grids has exposed critical limitations in conventional capacity pricing mechanisms, which calculate charges based solely on monthly maximum demand without distinguishing when peak demand occurs. This approach fails to reflect the temporal value of capacity and provides insufficient incentives for demand-side optimization. To address these challenges, this paper proposes a time-of-use (TOU) capacity pricing method that integrates user load characteristics to enable more equitable cost allocation and optimized electricity consumption patterns. The methodology employs K-means clustering analysis of user load profiles to partition pricing periods, accurately capturing differential capacity value across temporal intervals. We validate the clustering approach through the elbow method and silhouette analysis, confirming k = 3 as optimal and demonstrating K-means superiority over hierarchical and density-based alternatives. This data-driven approach ensures that period delineation reflects actual consumption patterns of commercial and industrial users. A capacity cost allocation model is established using the Shapley value method, incorporating maximum demand in each designated period while maintaining revenue neutrality for the grid operator. The 80% load simultaneity factor is empirically validated using 12 months of Shanghai industrial data (May 2023–April 2024). A Stackelberg game-based pricing model for TOU capacity tariffs is developed, incentivizing users to deploy energy storage systems and optimize charging strategies. We prove game convergence theoretically and demonstrate equilibrium achievement within 3–5 iterations across diverse initialization scenarios. Energy storage capacity is optimized by sector (3.5–6.5% of peak demand) rather than uniformly, and realistic battery self-discharge rates (0.006%/hour) are incorporated. Case study analysis using real operational data from 11 commercial and industrial sub-sectors in Shanghai demonstrates effectiveness. Extended to 12 months with seasonal analysis, results show the proposed strategy reduces the peak-to-valley difference ratio by 2.4% 95% CI: 1.9%, 2.9%, p < 0.001; increases the system load factor by 1.3% 95% CI: 0.9%, 1.7%, p < 0.001; and achieves reductions in users’ total capacity costs of 3.6% 95% CI: −4.2%, −3.0%, p < 0.001. Comparative analysis shows the proposed method significantly outperforms simple TOU (improvement +1.2 pp) and peak-responsibility pricing (improvement +0.6 pp). Monte Carlo robustness analysis (1000 scenarios) confirms performance stability under demand uncertainty. This research provides theoretical foundations and practical methodologies for capacity cost allocation, offering valuable insights for policymakers and utilities seeking to enhance demand-side response mechanisms and improve power resource allocation efficiency.
Wang et al. (Fri,) studied this question.