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Open access Aug 2026

Single-level MILP incentive pricing for customer directrix load-based demand response in smart buildings

With the high penetration of renewable energy, tapping the regulation potential of smart buildings in distribution networks plays a pivotal role in enabling orderly renewable energy accommodation. Customer directrix load-based demand response serves as an effective mechanism for guiding smart building interaction. However, its incentive price, derived as the equilibrium point of a leader-follower game between the operator and load entities, relies on a corresponding bilevel optimization model that suffers from low computational efficiency. To address this limitation, an efficient incentive pricing method is proposed. The proposed linear similarity metric and incentive revenue formulation ensure the linearity of the lower-level optimization problem. Subsequently, based on primal-dual feasibility, an aggregated strong-duality equality, and a discrete-price reformulation, the original bilevel model is accurately reformulated into a single-level mixed-integer linear programming problem, enabling a one-shot determination of the incentive price. Simulation results demonstrate that the proposed linear metric is highly consistent with traditional nonlinear metrics in terms of ranking monotonicity. Compared with time-of-use-only demand response and fixed incentive pricing strategies, the proposed method can identify an economically balanced incentive price that effectively guides smart building energy consumption behavior, improves renewable energy accommodation, and maintains favorable economic performance for both the distribution system operator and smart buildings. These findings support the use of the proposed single-level MILP framework for balancing renewable energy accommodation with the economic interests of the distribution system operator and smart buildings.

Jianjun He, Xu-Dong Lei, Bo-Chun Zhan et al. · 0 citations
Conference Jul 2026

A Hierarchical Integrated Management Method for the Aggregated Control of Large-Scale Renewable Resources in Virtual Power Plants

A method for dynamic aggregation and regulation management of large-scale resources in a virtual power plant (VPP) is proposed. By determining the peak periods, off-peak periods, and normal periods of regional electricity consumption, the power system load demand data, flexible load characteristic data, and price data for each period are obtained. The operation objective function of VPP under the market mechanism is proposed, and its participation in the market operation mechanism is established. The types of flexible resources are identified, and a multi-flexible resource dynamic aggregation model of VPP is constructed. The improved wolf pack algorithm (WPA) is used to optimize the satisfaction factor of the satisfactory decision. The results show that compared with traditional methods, the improved WPA algorithm can significantly reduce costs, enabling VPP to meet electricity demand through gas turbines and energy storage equipment during peak periods, thereby enhancing the flexibility and economy of the power system.

Yujie Song, Zikang Wei, Weiqiang Lu et al. · 0 citations
Open access 2026

Two-Stage Optimization Scheduling Model for Flexible Resource Aggregation in High-Share Renewable Energy Power Systems Considering Multi-Type Demand Response

: Aiming at the prominent problems of insufficient coordination of multi-type flexible resources and insufficient utilization of demand response potential in high-proportion renewable energy power systems, this paper proposes a two-stage optimal scheduling model for flexible resource aggregation that integrates price-based and segmented incentive-based demand response. In the first stage, the price-based demand response is adopted to optimize the time distribution of elastic loads with the goal of minimizing the net load fluctuation, so as to smooth the net load curve. In the second stage, based on the optimized net load, the segmented incentive-based demand response market mechanism is combined with electrochemical energy storage, pumped storage and flexibility-transformed thermal power units to construct a scheduling model with the minimum system operation cost as the goal. The quadratic terms in the model are linearized by SOS2 constraints, and the Gurobi solver is used for efficient solution. The results show that the proposed model can reduce the net load variance by 46.5%, reduce the system operation cost by 2.33%, avoid the frequent start-stop of thermal power units, significantly enhance the system flexibility and renewable energy consumption capacity, and provide an effective scheduling solution for the safe and economic operation of new power systems.

Yong-Zhi-Song-,-Ding-Zeng-Zhou-,-Shan-Liu-,-Song-J Liu, Qiang Li, Qianpeng Hao et al. · 0 citations
Open access Jul 2026

Stackelberg Game-Based Optimal Clearing Mechanism for Heterogeneous Energy Storage in Frequency Regulation Markets

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.

Zhe-Kai Xu, Chun-Xiang Yang, Zi-Fen Han et al. · 0 citations
Open access Sep 2026

Two-Stage Optimal Scheduling for Virtual Power Plants Considering Scheduling Success Probability of Multi-Agent Demand-Side Resources

High penetration of renewable energy imposes greater demands on the scheduling flexibility of demand-side resources in virtual power plant (VPP) dispatch. Nevertheless, heterogeneous resources exhibit remarkable differences in response reliability, and electric vehicles (EVs) in particular show distinct execution performance between orderly charging and vehicle-to-grid (V2G) modes. To tackle this issue, this paper proposes a two-stage optimal scheduling strategy for multi-agent VPPs incorporating scheduling success probability. A quantitative model for the effective dispatch contribution coefficient is constructed from two dimensions, i.e., relative capacity weight and dispatch execution reliability, with differentiated parameters tailored for EV charging and V2G modes. The two-stage leader–follower game problem is decoupled via backward induction, and the optimal dispatch price is rigorously derived through Karush–Kuhn–Tucker conditions. A 24 h case study covering wind power, photovoltaics, energy storage, EVs, and air-conditioning loads validates the proposed method. Results indicate that the strategy boosts total VPP revenue by 7.43% compared with independent operation, lifts the renewable energy accommodation rate from 88.3% to 94.6%, and reduces the average operating cost by 19 CNY/MWh. Through dual-mode differentiated scheduling, EVs achieve 5.10% revenue growth and serve as a key flexible resource for VPP economic operation.

Yu-Kun Jin, Xiao-Peng Li, Si-Yuan Cai et al. · 0 citations
Conference Jul 2026

Optimal Operation of Virtual Power Plants with Energy Storage Based on Spot Market Profit and Evaluation

Under the background of energy transition and "dual carbon" goals in China, distributed new energy (DNE) and energy storage equipment's installed capacity has increased exponentially. As an efficient distributed resource management system, the virtual power plant has also garnered significant attention from domestic scholars and institutions. Extensive research has been conducted on a series of trading strategies for virtual power plants participating in the electricity spot market. With the expanding scale of virtual power plants involved in market-based trading, the operational evaluation of virtual power plants is set to become a key focus of attention. This paper proposes an operational optimization model aimed at enhancing the participation of generation-type virtual power plants with energy storage in the spot market and reducing prediction deviations. The model considers factors such as penalties for predicted power deviations, historical positive and negative power deviation of generation aggregation units, and energy storage charging and discharging efficiency. The paper analyzes and discusses the impacts under different evaluation intensities. When the system evaluation threshold is lowered and the unit deviation penalty coefficient is increased, the model effectively reduces assessment costs and improves the daily operational benefits in scenarios involving distributed virtual power plants with energy storage.

Kaiqing Liang, Xuebo Qiao, Xiangyang Su et al. · 0 citations

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