International Journal of Electrical Power & Energy Systems最新文献_第7页

Probabilistic multi objective planning of battery storage and mixed distributed generation for reliable and efficient grid connected distribution systems 可靠高效并网配电系统中电池储能与混合分布式发电的概率多目标规划

IF 5 2区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

International Journal of Electrical Power & Energy Systems

Pub Date : 2026-01-01 DOI: 10.1016/j.ijepes.2025.111542

Furqan Latif Memon , Aamir Ali , M.U. Keerio , Rameez Akbar Talani , Ghulam Abbas , Ali Elrashidi , Ezzeddine Touti

This study addresses the challenge of optimally planning distributed energy resources in grid-connected distribution systems under significant uncertainty in renewable generation and load demand. As high penetration of wind, solar PV, and battery energy storage systems (BESS) increases variability and operational risks, developing a robust long-term planning framework is essential for ensuring economic efficiency, technical reliability, and environmental sustainability. To tackle this, a stochastic mixed-integer nonlinear programming (MINLP) model is proposed, incorporating probabilistic representations of wind speed, solar irradiance, load profiles, and market energy prices using Weibull, lognormal, and normal distributions. Monte Carlo Simulation combined with a Backward Reduction Algorithm is used to generate representative scenarios. A hybrid evolutionary optimisation approach—integrating Genetic Algorithm (GA), Particle Swarm Optimisation (PSO), and Differential Evolution (DE)—is developed to solve the multi-objective problem. The framework simultaneously minimises cost, emissions, power losses, voltage deviation, and enhances reliability and voltage stability. Application to the IEEE 33-bus and 118-bus systems demonstrates substantial improvements: cost reductions up to 19.3%, emission reduction up to 80.9%, and significant improvements in network losses, voltage profiles, and reliability indices. The results confirm that coordinated planning of dispatchable DGs, renewable DGs, and BESS yields a resilient, economical, and sustainable solution for future smart distribution networks.

本研究解决了在可再生能源发电和负荷需求存在显著不确定性的情况下，并网配电系统中分布式能源的优化规划所面临的挑战。随着风能、太阳能光伏和电池储能系统（BESS）的高渗透率增加了可变性和运营风险，制定一个强大的长期规划框架对于确保经济效率、技术可靠性和环境可持续性至关重要。为了解决这个问题，提出了一个随机混合整数非线性规划（MINLP）模型，该模型结合了风速、太阳辐照度、负荷分布和市场能源价格的概率表示，使用威布尔分布、对数正态分布和正态分布。采用蒙特卡罗模拟结合后向约简算法生成具有代表性的场景。结合遗传算法（GA）、粒子群算法（PSO）和差分进化算法（DE），提出了一种混合进化优化方法来解决多目标问题。该框架同时最大限度地降低了成本、排放、功率损耗、电压偏差，并提高了可靠性和电压稳定性。在IEEE 33总线和118总线系统上的应用显示出了显著的改进：成本降低高达19.3%，排放量减少高达80.9%，网络损耗、电压分布和可靠性指标也有了显著改善。结果证实，可调度dg、可再生dg和BESS的协调规划为未来的智能配电网络提供了一个有弹性、经济和可持续的解决方案。

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引用次数: 0

Dynamic Event-Triggered Fixed-Time Distributed Secondary Control for DC Microgrids under Control Signal Uncertainty 控制信号不确定下的直流微电网动态事件触发定时分布式二次控制

IF 5 2区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

International Journal of Electrical Power & Energy Systems

Pub Date : 2026-01-01 DOI: 10.1016/j.ijepes.2025.111449

Kamran Etivand, Mohsen Kalantar

DC microgrids face fundamental challenges in achieving simultaneous voltage regulation and current sharing. While conventional consensus-based secondary controllers overcome droop limitations, they suffer from slow asymptotic convergence and a high communication burden due to continuous, time-triggered data exchange. Finite-time consensus-based controllers, though faster, remain practically constrained by their dependence on initial conditions. This paper proposes a distributed fixed-time secondary control scheme, co-designed with a dynamic event-triggered communication mechanism. The proposed controller ensures exact bus-voltage restoration and accurate current sharing among Distributed Generation Units within a fixed settling time, independent of initial conditions, and is robust against control signal uncertainties. The dynamic event-triggered mechanism substantially reduces communication among Distributed Generation Units while maintaining overall microgrid stability. Rigorous Lyapunov-based analysis confirms the system’s fixed-time stability. In addition, the proposed event-triggering mechanism is shown to exclude Zeno behavior. Comprehensive MATLAB/Simulink simulations validate the proposed controller’s effectiveness, robustness to uncertainties, and superior performance across diverse operational scenarios.

直流微电网在实现同步电压调节和电流共享方面面临着根本性的挑战。虽然传统的基于共识的二级控制器克服了下垂限制，但由于连续的、时间触发的数据交换，它们存在缓慢的渐近收敛和较高的通信负担。基于有限时间共识的控制器虽然速度更快，但实际上仍然受到它们对初始条件的依赖的限制。本文提出了一种与动态事件触发通信机制协同设计的分布式固定时间辅助控制方案。该控制器能够保证在固定的稳定时间内精确的总线电压恢复和分布式发电机组之间精确的电流共享，与初始条件无关，并且对控制信号的不确定性具有鲁棒性。动态事件触发机制大大减少了分布式发电机组之间的通信，同时保持了微电网的整体稳定性。严格的李雅普诺夫分析证实了系统的定时稳定性。此外，所提出的事件触发机制被证明可以排除芝诺行为。全面的MATLAB/Simulink仿真验证了所提控制器的有效性、对不确定性的鲁棒性以及在不同操作场景下的卓越性能。

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引用次数: 0

Enhancing microgrid profitability: ISSA-based optimization of thermal and renewable energy management with CHP considerations 提高微电网的盈利能力：基于issa优化热电联产的热能和可再生能源管理

IF 5 2区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

International Journal of Electrical Power & Energy Systems

Pub Date : 2026-01-01 DOI: 10.1016/j.ijepes.2025.111423

Yan Jiang

This study develops a green-finance–oriented optimization framework for microgrid operation by integrating thermal units, renewable energy, and CHP systems using the Integrated Swarming Strategy Algorithm (ISSA). Four planning scenarios—probabilistic and randomized, with and without CHP—are evaluated under variable market prices and environmental constraints. ISSA achieved a 95.28 % success rate in reducing operational costs and consistently generated higher profits when aligned with carbon pricing and renewable subsidy mechanisms. The results show that combining ISSA optimization with green finance incentives significantly enhances microgrid profitability and sustainability. Future work will focus on climate-adaptive heating loads and carbon–neutral planning.

本研究利用集成群策略算法（Integrated swarm Strategy Algorithm， ISSA）整合热电机组、可再生能源和热电联产系统，为微电网运行开发了一个以绿色金融为导向的优化框架。在可变的市场价格和环境约束下，评估了四种规划情景——概率和随机，有和没有热电联产。ISSA在降低运营成本方面取得了95.28%的成功率，并在与碳定价和可再生能源补贴机制相结合的情况下持续产生更高的利润。结果表明，将ISSA优化与绿色金融激励相结合，可以显著提高微电网的盈利能力和可持续性。未来的工作将侧重于气候适应性热负荷和碳中和规划。

引用次数: 0

Defender–attacker–defender model for power system resilience enhancement with protection invalidity and transmission switching 考虑保护失效和传输切换的电力系统弹性增强防御-攻击-防御模型

IF 5 2区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

International Journal of Electrical Power & Energy Systems

Pub Date : 2026-01-01 DOI: 10.1016/j.ijepes.2025.111548

Yuxiong Huang, Hongrui Lu, Chenwei Gao, Xuanman Rong, Gengfeng Li, Zhaohong Bie

The defender–attacker–defender (DAD) model is widely used for the robust resilience enhancement of power systems. However, previous studies fail to account for time-varying component failure probabilities and assume invulnerable pre-event defenses. While this simplification avoids decision-dependent uncertainty (DDU) between decision-making stages, it introduces decision bias. Additionally, the benefits of chronological transmission switching (CTS) for in-event disaster mitigation remain underexplored. To address these issues, this paper integrates CTS into the DAD model’s in-event stage and employs probabilistic rather than deterministic criteria for damage scenario modeling. A hypothetical attack decision variable is introduced to reformulate the classical DAD structure, transforming DDU into decision-independent uncertainty (DIU). This modification eliminates the interaction between protection decisions and component failure rates. To effectively solve the model, a nested column-and-constraint generation (N-C&CG) algorithm is proposed. Extensive case studies on the IEEE RTS-79 test system and IEEE 118-bus system validate the effectiveness of the proposed approach.

防御者-攻击者-防御者（DAD）模型被广泛用于电力系统的鲁棒弹性增强。然而，以往的研究未能考虑时变部件的失效概率，并假设了无懈可击的事前防御。虽然这种简化避免了决策阶段之间的决策依赖不确定性（DDU），但它引入了决策偏差。此外，时序传输交换（CTS）在事件减灾方面的好处仍未得到充分探索。为了解决这些问题，本文将CTS集成到DAD模型的事件阶段，并采用概率标准而不是确定性标准进行损伤情景建模。引入假设的攻击决策变量，对经典的攻击决策变量结构进行重新表述，将攻击决策变量转化为决策独立不确定性（DIU）。这种修改消除了保护决策和组件故障率之间的相互作用。为了有效求解该模型，提出了一种嵌套列约束生成（N-C&；CG）算法。对IEEE RTS-79测试系统和IEEE 118总线系统进行了广泛的案例研究，验证了所提出方法的有效性。

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引用次数: 0

A data-physics hybrid driven fault identification model integrating multivariate fault information of wind farm 集成多变量风电场故障信息的数据-物理混合驱动故障识别模型

IF 5 2区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

International Journal of Electrical Power & Energy Systems

Pub Date : 2026-01-01 DOI: 10.1016/j.ijepes.2025.111508

Jiaze Yang , Zengping Wang , Zexin Zhou , Tong Wang

Due to the fault characteristics of renewable energy source such as limited short-circuit current amplitude and controlled phase angle, the traditional relay protection based on the power frequency short-circuit characteristics of synchronous generator power supplies faces issues such as complex adaptive setting coordination and insufficient interactive coordination of judgment principles. In view of the current situation that traditional rely protection is not adaptable enough after the renewable energy source access, starting from the wind farm information fusion strategy, a data-physics hybrid driven fault identification model with Phasor-Aware Graph Sampling and Aggregation Network as the main body and embedded in the physical prior constraints of the power system is constructed, which takes the real-complex dual-domain feature deep mining of multi-point electrical phasor information of the wind farm and the overall idea of fusion decision of the field global feature, and constructs the graph sampling mechanism and regularization strategy that embeds wind farm topology and physical formulas, in order to further improve the model’s generalization ability and understanding of the physical distribution law of the power system. Finally, the adaptability and effectiveness of the proposed identification model is verified by experimental results, which show that the identification model can improve the accuracy of fault identification under special fault conditions with weak fault characteristics and variable topological conditions. © 2017 Elsevier Inc. All rights reserved.

由于可再生能源具有短路电流幅值有限、相位角可控等故障特征，传统的基于同步发电机电源工频短路特性的继电保护面临自适应整定协调复杂、判断原则交互协调不足等问题。针对可再生能源接入后传统依赖保护适应性不足的现状，从风电场信息融合策略出发，构建了以相量感知图采样与聚合网络为主体，嵌入电力系统物理先验约束的数据-物理混合驱动故障识别模型。采用对风电场多点电相信息的实复双域特征深度挖掘和现场全局特征融合决策的总体思路，构建嵌入风电场拓扑和物理公式的图采样机制和正则化策略，以进一步提高模型的泛化能力和对电力系统物理分布规律的理解。最后，通过实验验证了所提识别模型的适应性和有效性，表明该识别模型能够提高故障特征弱、拓扑条件变的特殊故障条件下的故障识别精度。©2017 Elsevier Inc.版权所有。

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引用次数: 0

Hierarchical energy flexibility coordination of all-electric buildings for deliverable grid services 面向可交付电网服务的全电建筑分层能源灵活性协调

IF 5 2区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

International Journal of Electrical Power & Energy Systems

Pub Date : 2026-01-01 DOI: 10.1016/j.ijepes.2025.111476

Sevda Zeinal Kheiri, Mohammad Amin Mirzaei, Masood Parvania

Building electrification, combined with smart technologies and distributed energy resources, not only reduces the carbon footprint of buildings but also transforms them into active participants in grid operations by providing essential flexibility services and grid support. This paper proposes a hierarchical optimization framework that effectively bridges the gap between the energy flexibility potential of all-electric buildings and power grid support by ensuring that the available energy flexibility is transformed into technically feasible and deliverable energy services through distribution networks while respecting both network constraints and occupant comfort requirements. Local controllers operated by aggregators first optimize zone-level energy flexibility in a day-ahead scheduling framework by coordinating cold-climate air source heat pumps (ccASHPs), heat pump water heaters (HPWHs), photovoltaic (PV) systems, and energy storage systems across multiple all-electric buildings within their respective zones. A central controller operated by the distribution system operator (DSO) then optimizes the energy flexibility offered to the day-ahead energy market by aggregating zone-level energy flexibility and considering distribution network constraints including voltage limits, line capacity restrictions, and power losses to ensure deliverable energy flexibility to the Independent System Operator (ISO). The approach integrates thermal dynamics of heating and cooling loads with electrical characteristics of distributed energy resources to enable coordinated energy flexibility provision that maintains occupant comfort through controlled indoor and water temperatures. The simulation results show reductions in DSO operation costs and electricity bills of the buildings while enabling the provision of deliverable energy flexibility to the ISO.

建筑电气化与智能技术和分布式能源相结合，不仅减少了建筑物的碳足迹，而且通过提供必要的灵活性服务和电网支持，将建筑物转变为电网运营的积极参与者。本文提出了一个分层优化框架，通过确保可用的能源灵活性通过配电网络转化为技术上可行和可交付的能源服务，同时尊重网络约束和居住者舒适度要求，有效地弥合了全电动建筑能源灵活性潜力与电网支持之间的差距。由聚合器操作的本地控制器首先通过协调寒冷气候空气源热泵（ccashp）、热泵热水器（HPWHs）、光伏（PV）系统和储能系统，在各自区域内的多个全电动建筑中优化区域级能源灵活性。然后，由配电系统运营商（DSO）操作的中央控制器通过汇总区域级能源灵活性并考虑配电网络约束（包括电压限制、线路容量限制和功率损耗）来优化向日前能源市场提供的能源灵活性，以确保向独立系统运营商（ISO）提供能源灵活性。该方法将加热和冷却负荷的热动力学与分布式能源的电气特性相结合，通过控制室内温度和水温来实现协调的能源灵活性，从而保持居住者的舒适度。模拟结果显示，DSO的运作成本和楼宇电费均有所减少，同时可为ISO提供灵活的可交付能源。

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引用次数: 0

Deriving linear and nonlinear demand models responsive to cultural signals for assessing demand-side flexibility 建立响应文化信号的线性和非线性需求模型，以评估需求侧灵活性

IF 5 2区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

International Journal of Electrical Power & Energy Systems

Pub Date : 2026-01-01 DOI: 10.1016/j.ijepes.2025.111499

Mohammad Musa Mohammadi, Mahmoud Reza Haghifam, Sayyed Majid Miri Larimi

With the advancement of technology and the movement of power systems towards smartness and the need to reduce emissions, the power system will be subject to the widespread use of renewable energy sources(RES) and smart electrical equipment on the demand side, which will increase the uncertainties in the system on both the generation and demand sides. The use of demand-side flexibility(DSF) can deal with the uncertainty in the power system. By assessing demand-side flexibility, the regulator can examine the participation of end-users in demand response(DR) programs and demand response cultural programs. In this paper, the assessment of DSF is developed based on the simultaneous modeling of demand response programs and demand response cultural programs. The behavior of the derived models is investigated in response to changes in demand price elasticity, demand cultural elasticity, electricity price, reward/penalty, and variations in the number of cultural signals. In order to investigate the performance of the proposed models, numerical studies have been conducted on the real-world Romanian electricity grid. The results show that DSF is highly dependent on the degree of demand price elasticity and demand cultural elasticity. So that, by doubling the price elasticity and the real-time price at peak consumption, the reduction in peak consumption and energy in the linear model will be 22.16 % and 2.22 %, respectively. Also, by doubling the demand cultural elasticity, and the number of cultural signals at peak consumption, the reduction in peak consumption and energy in the linear model will be 9.82 % and 0.94 %, respectively.

随着技术的进步和电力系统向智能方向发展以及减少排放的需要，电力系统将在需求侧广泛使用可再生能源（RES）和智能电气设备，这将增加发电和需求侧系统的不确定性。需求侧灵活性（DSF）的应用可以解决电力系统中的不确定性问题。通过评估需求侧灵活性，监管者可以检查终端用户在需求响应（DR）计划和需求响应文化计划中的参与情况。本文在需求响应计划和需求响应文化计划同时建模的基础上，开发了DSF的评估方法。在需求价格弹性、需求文化弹性、电价、奖惩和文化信号数量变化的影响下，研究了所得模型的行为。为了研究所提出的模型的性能，对实际的罗马尼亚电网进行了数值研究。结果表明，DSF高度依赖于需求价格弹性和需求文化弹性的程度。因此，通过将价格弹性和峰值实时电价加倍，线性模型中的峰值用电量和能源分别减少22.16%和2.22%。此外，通过将需求文化弹性和峰值消费时的文化信号数量增加一倍，线性模型中的峰值消费和能量减少分别为9.82%和0.94%。

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引用次数: 0

Dual-decoupling of deep reinforcement learning reward function for integrated energy system scheduling: A collaborative mechanism of constraint separation and hierarchical decision-making 综合能源系统调度的深度强化学习奖励函数双解耦：约束分离与分层决策的协同机制

IF 5 2区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

International Journal of Electrical Power & Energy Systems

Pub Date : 2026-01-01 DOI: 10.1016/j.ijepes.2025.111467

Xiangyan Yang , Shaobing Yang , Liang Hu , Peng Peng , Mingli Wu

Deep reinforcement learning (DRL) applied to the integrated energy system (IES) scheduling tasks often leads to reward functions composed of multiple coupled components due to the complex structure of IES. However, reward design determines how agents perceive task objectives and action values, and excessive reward terms can cause policy confusion, resulting in suboptimal optimization. To address the multi-objective reward coupling challenge in IES optimal scheduling, this study proposes a DRL method based on a dual decoupling mechanism for reward functions. At the algorithmic level, this method reconstructs the Markov Decision Process (MDP) as a Constrained Markov Decision Process (CMDP) and introduces two improved algorithms, LTD3 and LSAC, combining dual decomposition to separate economic objectives from safety constraints in reward functions. At the architectural level, a hierarchical reinforcement learning framework (LTD3-LSAC) is established to decouple decision-making for electric units and thermal units, thereby separating electrical and thermal components in reward functions. Through a collaborative technical pathway combining horizontal algorithmic improvement and vertical architectural optimization, the proposed DRL method achieves dual decoupling of reward functions in IES scheduling tasks. Two-stage ablation experiment results show that the proposed LTD3-LSAC framework effectively improves the operational economy of IES: the total operational cost is reduced by 13.28% compared with the traditional strong penalty method, while the cumulative constraint violation index is controlled at 4.21, which is much lower than 36.78 of the weak penalty method; compared with the single-layer architecture, the hierarchical strategy further reduces the total operational cost by 3.23%. These results verify the superiority of the proposed dual decoupling mechanism in this study from the two dimensions of constraint handling and multi-energy coordination, respectively.

由于综合能源系统（IES）结构复杂，将深度强化学习（DRL）应用于调度任务时，往往导致奖励函数由多个耦合组件组成。然而，奖励设计决定了代理如何感知任务目标和行动价值，过多的奖励条款可能导致策略混乱，导致次优优化。为解决IES最优调度中的多目标奖励耦合问题，提出了一种基于奖励函数双解耦机制的DRL方法。在算法层面，该方法将马尔可夫决策过程（MDP）重构为约束马尔可夫决策过程（CMDP），并引入LTD3和LSAC两种改进算法，结合对偶分解将奖励函数中的经济目标与安全约束分离。在体系结构层面，建立了分层强化学习框架（LTD3-LSAC）来解耦电单元和热单元的决策，从而分离奖励函数中的电和热组件。本文提出的DRL方法通过横向算法改进和纵向架构优化相结合的协同技术路径，实现了IES调度任务中奖励函数的双重解耦。两阶段烧烧实验结果表明，提出的LTD3-LSAC框架有效提高了IES的运行经济性：与传统的强惩罚方法相比，总运行成本降低了13.28%，累计约束违反指数控制在4.21，远低于弱惩罚方法的36.78；与单层架构相比，分层策略进一步降低了总运营成本3.23%。这些结果分别从约束处理和多能协调两个维度验证了本文提出的双解耦机制的优越性。

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引用次数: 0

Enhanced control of energy storage converter for stabilizing renewable energy integrated systems 为稳定可再生能源集成系统而加强储能变流器控制

IF 5 2区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

International Journal of Electrical Power & Energy Systems

Pub Date : 2026-01-01 DOI: 10.1016/j.ijepes.2025.111554

Lei Gao , Jing Lyu , Weian Wang , Guodong Chen , Han Wang , Xu Cai

The increasing penetration of renewable energy sources has raised the risk of wideband oscillations in renewable energy integrated systems. However, applying existing oscillation suppression methods to individual units in renewable power plants presents significant challenges. With the rapid advancement of energy storage technology, if the control strategy is properly designed, energy storage converters can effectively address oscillatory stability issues. To this end, an enhanced control integrating self-stabilization and power decoupling capabilities for power control-based energy storage converters is proposed to improve the oscillation stability of renewable energy integrated systems. First, a power-domain admittance model is established to analyze the power coupling characteristics of power control-based energy storage converter. The relationship between power coupling and oscillatory stability is then elucidated. Subsequently, the insufficient self-power decoupling ability of power control-based energy storage converters under weak grid conditions is examined. It is determined that reducing power coupling is crucial for addressing oscillatory stability issues. On this basis, the structure, parameters design, and power decoupling capability of the enhanced control strategy are analyzed and verified. Finally, the effectiveness of the proposed strategy is validated through a case study of a practical renewable energy integrated system under various operating conditions using PSCAD/EMTDC simulations.

可再生能源的日益普及增加了可再生能源综合系统宽带振荡的风险。然而，将现有的振动抑制方法应用于可再生能源发电厂的单个机组存在重大挑战。随着储能技术的飞速发展，如果控制策略设计得当，储能变换器可以有效地解决振荡稳定性问题。为此，提出了一种集自稳定和功率解耦能力于一体的基于功率控制的储能变流器增强控制，以提高可再生能源集成系统的振荡稳定性。首先，建立功率域导纳模型，分析基于功率控制的储能变换器的功率耦合特性。然后阐明了功率耦合与振荡稳定性之间的关系。随后，研究了基于功率控制的储能变换器在弱电网条件下的自解耦能力不足的问题。确定减小功率耦合对于解决振荡稳定性问题至关重要。在此基础上，对增强控制策略的结构、参数设计和功率解耦能力进行了分析和验证。最后，通过PSCAD/EMTDC仿真，对实际可再生能源集成系统在不同运行条件下的有效性进行了验证。

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引用次数: 0

Non-cooperative game theoretic-based two-stage nested optimization model for energy hub pricing and management considering extreme conditions 极端条件下基于非合作博弈理论的能源枢纽定价与管理两阶段嵌套优化模型

IF 5 2区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

International Journal of Electrical Power & Energy Systems

Pub Date : 2026-01-01 DOI: 10.1016/j.ijepes.2025.111528

Shuo Feng , Jun Xie , Yuanyu Ge , Denghui Fu , Jiaqi Chang

Extreme conditions pose severe challenges to the reliable operation of energy systems. In this context, the energy hub (EH) effectively integrates heterogeneous energy, facilitating strategic decision-making of energy producers and consumers, while also bringing opportunities to improve the sustainable power supply capacity of the energy system in extreme conditions. This paper characterizes the resilience of EH via minimum load loss as a key metric conditions, and establishes an innovative two-stage nested optimization model to achieve the synergistic optimization of the economic objectives and sustainable power supply capabilities of EH operators (EHO). In modeling, the diversity of Nash equilibrium (NE) is emphasized, and the resilience of EH is maximized through the collaborative supply of heterogeneous energy sources while ensuring NE. Specifically, a bilevel Stackelberg game (BSG) is formulated in the first stage to derive numerical characteristics of NE, which are subsequently embedded into the second-stage model along with the NE constraints and BSG framework. In solving, the BSG is transformed into a tractable form through the application of Karush-Kuhn-Tucker (KKT) optimality conditions, duality theory, and linearization techniques. Finally, a multi-objective optimization problem is formulated to explore the mapping between economic goals and sustainable power supply capacity, and an interval division-based fixed-step search algorithm (IDFSA) is proposed for its solution. The results show that the proposed strategy improves the economic benefits of EHO by 4.1%, 2.5%, 2.7%, and 4.9% in different scenarios, and can reduce the load loss by up to 22.5% in the most extreme scenario. Furthermore, sensitivity analysis indicates that the economic benefits of the EH are significantly influenced by the comfort sensitivity of electricity consumers (EC), while the number of electric vehicles (EV) has a relatively minor impact on the electricity costs of EC.

极端条件对能源系统的可靠运行提出了严峻的挑战。在此背景下，能源枢纽（EH）有效地整合了异质能源，促进了能源生产者和消费者的战略决策，同时也为提高极端条件下能源系统的可持续供电能力带来了机会。本文以最小负荷损失为关键指标条件，刻画了EH的弹性特征，并建立了创新的两阶段嵌套优化模型，实现了EH运营商经济目标和可持续供电能力的协同优化。在建模中，强调纳什均衡的多样性，在保证纳什均衡的前提下，通过异构能源的协同供应，使纳什均衡的弹性最大化。具体来说，在第一阶段，我们制定了一个双层Stackelberg博弈（BSG）来推导网元的数值特征，随后将其与网元约束和BSG框架一起嵌入到第二阶段模型中。在求解中，通过应用Karush-Kuhn-Tucker （KKT）最优性条件、对偶理论和线性化技术，将BSG转化为可处理的形式。最后，提出了一个多目标优化问题，探索经济目标与可持续供电能力之间的映射关系，并提出了基于区间划分的固定步长搜索算法（IDFSA）求解该问题。结果表明，在不同情景下，该策略可将EHO的经济效益分别提高4.1%、2.5%、2.7%和4.9%，在最极端情景下可将负荷损失降低22.5%。此外，灵敏度分析表明，电力消费者的舒适性敏感性显著影响电动汽车的经济效益，而电动汽车的数量对电动汽车的电力成本的影响相对较小。

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