The surging integration of volatile renewable energy severely exacerbates power grid frequency fluctuations, yet conventional frequency regulation (FR) market clearing mechanisms fail to efficiently coordinate heterogeneous energy storage systems (ESSs) due to the complete decoupling of multi-dimensional physical performance from economic dispatch. To resolve this critical industry bottleneck, this paper proposes a novel Stackelberg game-based clearing mechanism tailored for diverse ESS participation. A bi-level optimization framework is constructed to internalize physical FR characteristics into market economics; the upper level minimizes the system operator’s total procurement costs by transforming multi-dimensional physical metrics—including dynamic response rates, time delays, and control accuracy—into endogenous performance penalty factors. Concurrently, the lower level maximizes the individual revenues of heterogeneous ESS aggregators under a Gini coefficient-based fairness constraint to mitigate profit monopolization and promote a more sustainable market ecology. To address the computational challenges of high-dimensional non-convexity, an enhanced hybrid Genetic Algorithm and Quadratic Programming (GA-QP) solver is developed to secure robust convergence to the Stackelberg equilibrium. Comprehensive simulation results confirm that the proposed Stackelberg game-based clearing mechanism enables a highly rational, quality-driven allocation of frequency regulation capacity. By dynamically linking physical performance metrics with economic benefit factors, it successfully achieves an optimal balance of interests between heterogeneous energy storage aggregators and the overarching market. Crucially, compared to conventional purely economic models, this mechanism structurally prevents absolute technology monopoly—drastically reducing the market Gini coefficient from a hazardous 0.85 to a healthy 0.32—while sustaining multi-party equity at a negligible system cost increase of only 1.64%. Ultimately, this framework offers a highly feasible and resilient solution for the efficient clearing of multi-type energy storage in modern power systems.
Modern power systems face new challenges in maintaining stability and real-time balance with the large-scale integration of intermittent renewable energy. To address the persistent issue of insufficient participation in demand-side management, this study proposes a three-tier Stackelberg game coordination framework for Virtual Power Plants (VPPs) and Price-Based Demand Response (PBDR). To efficiently solve the high-dimensional nested multilevel optimization problem, a Hierarchical Nested Particle Swarm Optimization (HN-PSO) algorithm is developed. Theoretical analysis and simulation results demonstrate the existence and uniqueness of the global equilibrium in the proposed game model. A 24-hour simulation further shows that the VPP can mitigate price volatility while balancing internal dispatchable generation and external procurement. Therefore, the proposed approach can provide an efficient and practical computational method for decentralized market dispatch under renewable energy uncertainty.
Yi-Xiao Wang, Yunhui Chen, Bobo Chen et al.· International Journal of Swa...· 0 citations
Renewable-energy fluctuations and the conflicting economic objectives of independent stakeholders pose simultaneous physical and market challenges to the operation of flexible integrated energy systems (FIESs). To address these issues, this paper develops a market–physical coupled Stackelberg game-based coordinated operation framework incorporating the intertemporal flexibility of electrical and thermal energy storage. The integrated energy operator (IEO) acts as the leader and determines the internal electricity and heat purchase and sale prices, while the multi-energy cogeneration system (MECS) operator and the load aggregator act as followers and independently optimize generation-storage schedules and demand-response decisions, respectively. The load-aggregator response is formulated as a quadratic programming problem, whereas the MECS-side problem is formulated as a mixed-integer quadratic programming problem because of the binary storage-state variables. A nested Differential Evolution–CPLEX solution framework is employed to obtain a numerical Stackelberg equilibrium solution. A 24-h typical winter-day case study demonstrates the effectiveness of the proposed strategy. The peak electrical load decreases from 1845 kW to 1515 kW, corresponding to a reduction of 17.89%, while the peak-to-valley difference is reduced by 45.26%. The total user energy-purchasing cost decreases by 8.56%. Although the total electricity purchased from the external grid increases by 15.61%, the corresponding purchasing cost decreases by 30.98%, indicating that the coordinated strategy restructures grid transactions toward lower-price periods rather than simply minimizing grid imports. Comparative simulations with the no-storage and no-demand-response benchmark cases further confirm the complementary contributions of dual-storage flexibility and demand response to multi-agent economic performance. Moreover, the renewable curtailment rate is reduced from 6.51% to 0%, indicating that the proposed strategy enhances the local accommodation of wind-PV generation. These results show that the framework contributes to sustainable community energy operation by improving renewable-energy utilization, reducing peak-load pressure, lowering user energy expenditure, and supporting incentive-compatible coordination among independent stakeholders. Compared with conventional Stackelberg formulations that mainly focus on operator–user pricing or treat storage primarily as a balancing resource, the proposed framework explicitly embeds the intertemporal flexibility of electrical and thermal storage into the strategic response of the supply-side follower under endogenous multi-energy price signals.
Hai-Rui Hu, Peng Wen, Zhong Wang et al.· Sustainability· 0 citations
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
Decentralized energy communities (DECs) allow households, prosumers, and small generators to trade electricity locally, improving grid flexibility and supporting renewable integration. However, local market designs often face a trade-off between efficiency and fairness. Efficiency-oriented settlement rules can produce payment outcomes that are perceived as unfair, while strongly redistribution-based approaches may weaken incentives and reduce operational performance. This paper proposes a hybrid Vickrey-Clarke-Groves (VCG)-Shapley payment framework designed to balance an efficiency-oriented VCG settlement baseline, contribution-based fairness, and settlement stability. The VCG mechanism forms the efficiency-oriented settlement base, and a Shapley-inspired redistribution layer incentivizes meaningful community contributions beyond net energy supply. We develop a 14-factor contribution score to operationalize this approach, covering reliability, flexibility, self-consumption, demand response, renewable integration, transparency, and other supportive behaviors. Scores are evaluated every 30 minutes using time-varying weights to reflect the changing system conditions. A 24-hour simulation with generators, prosumers, and consumers compares the VCG-only settlement, the score-based redistribution, a convex combination payment and the proposed hybrid mechanism. The results show that the hybrid method produces the lowest SD and MAD-based payment dispersion among the evaluated post-VCG alternatives, preserves the VCG settlement anchor, and satisfies interval-level budget balance.
Kaung Si Thu, Pikkanate Angaphiwatchawal, S. Chaitusaney· IEEE Access· 0 citations
