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25 pages, 8930 KB

Open AccessArticle

A Two-Stage FF-RLS-Based Assessment Method for Frequency Support Capability of Grid-Following Wind and Photovoltaic Units

by Sudi Xu, Zijun Bin, Chenqing Wang, Xiangping Kong, Lei Gao, Zeyue Yang, Qi Wang, Hongqi Ding and Xiangqun Wang

Processes 2026, 14(18), 2977; https://doi.org/10.3390/pr14182977 (registering DOI) - 18 Sep 2026

Abstract

With the growing penetration of renewable energy, accurately characterizing the frequency support performance of grid-following wind and photovoltaic (PV) units has become increasingly important. However, conventional methods for assessing frequency support parameters often overlook practical dynamic effects, making it difficult to determine the [...] Read more.

With the growing penetration of renewable energy, accurately characterizing the frequency support performance of grid-following wind and photovoltaic (PV) units has become increasingly important. However, conventional methods for assessing frequency support parameters often overlook practical dynamic effects, making it difficult to determine the support parameters actually realized during disturbances. To address the time-domain coupling, differential noise amplification, and parameter distortion problems in the online identification of virtual primary frequency regulation and virtual inertia coefficients, this paper establishes a frequency response model for wind and PV units that incorporates these support mechanisms together with practical physical constraints. On this basis, a two-stage forgetting-factor recursive least squares (FF-RLS) method is proposed to identify realized frequency support parameters. Exploiting the difference in response time scales between primary frequency regulation and inertial support, a quasi-steady-state frequency regulation window and a transient inertia window are constructed to decouple the two parameters. Meanwhile, Tustin phase compensation and band-limited differentiation are introduced to mitigate measurement noise and the phase mismatch between frequency and power responses. Finally, a stable window criterion is developed to adaptively extract reliable identification intervals. Simulation studies on a modified IEEE 24 bus system, together with comparisons against conventional identification methods, demonstrate the effectiveness and accuracy of the proposed method. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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37 pages, 5914 KB

Open AccessArticle

Projection-Iterative-Method-Based Coordinated Power Control for Renewable-Rich Islanded Microgrids

by Yuemeng Wang and Qiming Sun

Processes 2026, 14(17), 2789; https://doi.org/10.3390/pr14172789 - 30 Aug 2026

Viewed by 306

Abstract

High renewable-energy penetration introduces rapid source-load variations and operating uncertainties into islanded microgrids, challenging conventional droop control in terms of dynamic frequency/voltage regulation and proportional power sharing. This paper proposes a coordinated control strategy integrating adaptive droop control, dynamic virtual impedance, and a [...] Read more.

High renewable-energy penetration introduces rapid source-load variations and operating uncertainties into islanded microgrids, challenging conventional droop control in terms of dynamic frequency/voltage regulation and proportional power sharing. This paper proposes a coordinated control strategy integrating adaptive droop control, dynamic virtual impedance, and a Projection-Iterative-Method-Based Optimizer (PIMO). A constrained multi-objective formulation coordinates active- and reactive-power-sharing errors, frequency and voltage deviations, virtual-impedance regularization, and parameter variation, while stability is enforced through Lyapunov- and eigenvalue-based feasibility criteria. PIMO periodically coordinates the droop coefficients and virtual-impedance parameters within prescribed feasible bounds. The proposed strategy is evaluated in MATLAB/Simulink under five-stage load transitions and renewable-rich scenarios covering PV penetration levels from 30% to 90%, irradiance and temperature variations, simultaneous source-load disturbances, and operating constraints. Compared with adaptive droop control, the proposed strategy reduces the full-window frequency and voltage RMSE by 9.4% and 26.6%, respectively. The active- and reactive-power-sharing errors decrease to 1.73% and 2.08%, while the worst-case settling time is reduced to 220 ms. In addition, PIMO achieves a mean execution time of 28.4 s within the adopted 60 s supervisory update interval. These results demonstrate improved dynamic regulation, proportional power sharing, and feasible supervisory optimization under renewable-rich operating conditions. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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27 pages, 3133 KB

Open AccessArticle

Adaptive Seamless Switching Strategy Considering Current Limiting for Renewable Energy Converters Based on PCC Condition Awareness

by Tao Tan, Zhishuang Wang, Yingyuan Zhang, Hao Xiao, Jiancheng Yu and Xia Shen

Processes 2026, 14(17), 2787; https://doi.org/10.3390/pr14172787 - 30 Aug 2026

Viewed by 291

Abstract

With the high penetration of renewable energy into power grids, grid-connected converters face severe challenges in adapting to wide-range variations of grid strength and suppressing fault overcurrents. A single grid-following (GFL) or grid-forming (GFM) control mode cannot ensure system stability across weak, moderately [...] Read more.

With the high penetration of renewable energy into power grids, grid-connected converters face severe challenges in adapting to wide-range variations of grid strength and suppressing fault overcurrents. A single grid-following (GFL) or grid-forming (GFM) control mode cannot ensure system stability across weak, moderately weak, and strong grid conditions, while the lack of current limiting measures may lead to damage to power electronic devices. To address these issues, an adaptive seamless switching strategy (ASSS) considering current limiting is proposed in this paper. The ASSS integrates three core modules: harmonic injection-based impedance identification for short-circuit ratio (SCR) calculation, a state variable reset method for seamless mode switching, and a hysteresis switching criterion to avoid frequent mode transitions. Besides ASSS, an adaptive virtual impedance is employed for fault current suppression. Based on MATLAB/Simulink, simulation verifications are conducted under typical working conditions including grid voltage sags and large-scale SCR variations. The results show that the proposed strategy can limit the maximum fault current efficiently, realize seamless switching between GFL and GFM modes with waveform distortion rate less than 5%, and ensure stable system operation across the entire range of grid strength variations. This strategy effectively improves the fault ride-through capability, grid adaptability, and switching dynamic stability of grid-connected converters, providing a reliable control solution for high-penetration renewable energy integration. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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23 pages, 1426 KB

Open AccessArticle

Dynamic Resource Allocation and Coordinated Dispatch of Wind–Solar-Storage Energy Systems Based on a Source–Load Association Graph

by Xiuyu Wu, Honghua Xu, Zijian Hu and Ye Ji

Processes 2026, 14(15), 2469; https://doi.org/10.3390/pr14152469 - 31 Jul 2026

Viewed by 399

Abstract

This study proposes dynamic resource allocation and coordinated dispatch based on a source–load association graph for an electric–gas–heat system with wind, photovoltaics, fixed and mobile storage, power-to-gas (P2G), combined heat and power (CHP), and soft open points (SOPs). At each operating update, storage [...] Read more.

This study proposes dynamic resource allocation and coordinated dispatch based on a source–load association graph for an electric–gas–heat system with wind, photovoltaics, fixed and mobile storage, power-to-gas (P2G), combined heat and power (CHP), and soft open points (SOPs). At each operating update, storage states, mobile-storage location and availability, and forecast profiles determine five typed relations and the subgraph classifications. Capacity-weighted centering then maps the state scores to time-varying device bounds without changing installed capacities or locations. The coordinated dispatch is formulated as a mixed-integer second-order cone program with SOC DistFlow constraints and an SOS2 gas-flow approximation. For the normal operating day, graph-guided dispatch yields an operating cost of 51,996.84 CNY, compared with 52,294.33 CNY for static equal-budget allocation and 52,829.05 CNY for topology-only allocation. The corresponding reductions are 0.5689% and 1.5753%, respectively, while all three policies serve 100% of demand and use 100% of available renewable energy within numerical tolerance. The graph-guided solution reaches a 0.0340% optimality gap, supporting its operating-cost advantage for the tested day. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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24 pages, 3608 KB

Open AccessArticle

Hierarchical Adjustable Potential Assessment of Electric Vehicles for Transmission–Distribution–Microgrid Coordination

by Mingshen Wang, Wenjun Ruan, Yi Pan, Xiaodong Yuan, Haiqing Gan and Kemin Dai

Processes 2026, 14(10), 1672; https://doi.org/10.3390/pr14101672 - 21 May 2026

Viewed by 453

Abstract

Electric vehicles (EVs) provide fast charging/discharging flexibility; however, single-layer assessments may overestimate the flexibility that can be physically delivered under downstream distribution-network constraints. This paper proposes a process-oriented hierarchical adjustable-potential assessment framework for transmission–distribution–microgrid coordination. At the microgrid/station layer, a chance-constrained vehicle feasible [...] Read more.

Electric vehicles (EVs) provide fast charging/discharging flexibility; however, single-layer assessments may overestimate the flexibility that can be physically delivered under downstream distribution-network constraints. This paper proposes a process-oriented hierarchical adjustable-potential assessment framework for transmission–distribution–microgrid coordination. At the microgrid/station layer, a chance-constrained vehicle feasible set is constructed to capture user uncertainty, and probabilistic Minkowski-sum aggregation is used to obtain a station-level theoretical envelope. At the distribution layer, voltage and line-thermal constraints are modeled using LinDistFlow and intersected with the theoretical envelope to derive an effective potential satisfying network security limits. At the transmission layer, the effective feasible region is further packaged into a time-varying generalized-battery parameter set for consistent upward reporting without introducing dispatch optimization. In addition, a bottleneck truncation effect (BTE) metric is defined to quantify how distribution constraints reduce upstream-usable flexibility. Case studies show that hierarchical network constraints compress both peak EV flexibility and the all-day feasible-region area. Specifically, the microgrid-layer theoretical envelope reaches 432 kW on the charging side, 124 kW on the discharging side, and 3799 kWh in feasible-region area. After distribution-layer security clipping, the effective envelope becomes 299 kW, 124 kW, and 2063 kWh, corresponding to reductions of 30.79%, 0.00%, and 45.70%, respectively, relative to the microgrid layer. After transmission-layer packaging, the deliverable envelope is further reduced to 285 kW, 118 kW, and 1946 kWh, i.e., reductions of 34.03%, 4.84%, and 48.78%, respectively, relative to the microgrid baseline. These results demonstrate that the proposed workflow provides verifiable and time-varying deliverable capability boundaries for cross-layer EV flexibility assessment. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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18 pages, 1838 KB

Open AccessArticle

Risk-Averse Generation Maintenance Scheduling for Power Systems Based on Contagious Value-at-Risk

by Yizheng Li, Haiqiong Yi, Xiao Yang, Shichang Cui, Xueying Wang, Yihan Liu and Xinying Zhou

Processes 2026, 14(10), 1536; https://doi.org/10.3390/pr14101536 - 9 May 2026

Viewed by 374

Abstract

Accurate quantification of uncertainty risks is pivotal for enhancing the reliability of generation maintenance scheduling (GMS) in power systems. However, existing risk quantification methods predominantly focus on the aggregate impact of uncertainty on system-wide operational risks, failing to identify critical risk sources. This [...] Read more.

Accurate quantification of uncertainty risks is pivotal for enhancing the reliability of generation maintenance scheduling (GMS) in power systems. However, existing risk quantification methods predominantly focus on the aggregate impact of uncertainty on system-wide operational risks, failing to identify critical risk sources. This limitation hinders the secure and efficient operation of power systems with high penetration of renewable energy. To address this issue, we propose a risk-averse GMS approach for power systems based on contagious value-at-risk (CoVaR). Specifically, we first introduce the CoVaR theory to identify dominant risk sources affecting the secure operation of the system and derive a general analytical expression for CoVaR that incorporates integral terms of uncertain variables. Subsequently, a scenario-based linearization reconstruction strategy is developed to discretize these integral terms, and the complex CoVaR model is reformulated into a computationally tractable mixed-integer linear programming (MILP) model. On this basis, a new risk-averse GMS model embedded with CoVaR constraints is constructed. This model achieves precise identification of critical risk sources by quantifying and comparing the impacts of different risk sources on both system operational costs and risk costs. Finally, simulation results on the modified IEEE 24-bus power system and IEEE 118-bus power system demonstrate the effectiveness and superiority of the proposed approach. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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21 pages, 2828 KB

Open AccessArticle

Multi-Objective Coordinated Scheduling and Trading Strategy for Economy and Security of Source–Grid–Load–Storage Under High Penetration of Renewable Energy

by Xianbo Ke, Jinli Lv, Xuchen Liu, Yiheng Huang and Guowei Qiu

Processes 2026, 14(7), 1117; https://doi.org/10.3390/pr14071117 - 30 Mar 2026

Cited by 1 | Viewed by 595

Abstract

With the continuous integration of a large amount of renewable energy sources such as wind and solar power into the power system, the economic and secure scheduling of the power grid, as a crucial carrier for electricity transmission, becomes of paramount importance. However, [...] Read more.

With the continuous integration of a large amount of renewable energy sources such as wind and solar power into the power system, the economic and secure scheduling of the power grid, as a crucial carrier for electricity transmission, becomes of paramount importance. However, issues such as voltage fluctuations at grid nodes, low renewable energy consumption rates, and increased active power losses, caused by the widespread integration of high proportions of renewable energy, urgently need to be addressed. To effectively solve these problems, this paper proposes a multi-objective coordinated optimization scheduling method for the economy and security of source–grid–load–storage based on an effective scenario-screening approach. Firstly, an iterative self-organizing data analysis algorithm based on density noise application spatial clustering is designed to efficiently generate typical output scenarios for renewable energy sources such as wind and solar power. Meanwhile, to achieve low-carbon scheduling objectives, green certificate and carbon trading mechanisms are introduced. A multi-objective coordinated scheduling and trading model for the economy and security of large power grids, sources, loads, and storage is constructed with the goal of enhancing renewable energy consumption, and it is solved using the weight assignment method and an improved particle swarm optimization algorithm. Finally, the effectiveness and feasibility of the proposed method are validated and illustrated based on an improved IEEE standard node test system. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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20 pages, 3461 KB

Open AccessArticle

Stability Analysis for Parallel Grid-Connected Heterogeneous Converters via Three-Port State-Space Modeling

by Jiaqing Wang, Xudong Hu, Jinzhong Li, Tao Cheng, Leixin Liang, Yuanxin Wang and Yan Du

Processes 2026, 14(7), 1100; https://doi.org/10.3390/pr14071100 - 28 Mar 2026

Viewed by 618

Abstract

The hybrid parallel operation of the grid-following (GFL) converter and the grid-forming (GFM) converter has become a typical scenario in distribution networks. The vastly different control philosophies and dynamics between the two give rise to complex small-signal stability issues, especially under weak grids. [...] Read more.

The hybrid parallel operation of the grid-following (GFL) converter and the grid-forming (GFM) converter has become a typical scenario in distribution networks. The vastly different control philosophies and dynamics between the two give rise to complex small-signal stability issues, especially under weak grids. Traditional methods primarily rely on equivalent models or impedance-based approaches at fixed operating points, which struggle to reveal the system instability mechanisms when the capacity ratio between the two types of converters changes. This paper establishes a three-port dynamic average model for a grid-connected system with heterogeneous GFL-GFM converters. Using the participation factor analysis method, the system’s dominant modes are identified, and the key parameters influencing oscillations at different frequencies, as well as their formation processes, are revealed. Furthermore, a stability analysis method for variable capacity ratios is proposed. This method re-performs modal analysis based on the varying capacities of the GFM and GFL converters, revealing the dominant factors and influencing mechanisms of system instability during capacity transitions. Finally, a simulation model is built in PSCAD/EMTDC to verify the correctness of the proposed three-port model and the theoretical analysis results. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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19 pages, 1711 KB

Open AccessArticle

Joint Planning Method for Soft Open Points and Energy Storage in Hybrid Distribution Networks Based on Improved DC Power Flow

by Wei Luo, Chenwei Zhang, Xionghui Han, Fang Chen, Zhenyu Lv and Yuntao Zhang

Processes 2026, 14(6), 1013; https://doi.org/10.3390/pr14061013 - 21 Mar 2026

Viewed by 679

Abstract

Intelligent soft open points (SOPs) and energy storage systems (ESSs) are effective ways to absorb distributed new energy in the spatial and temporal dimensions, and play an important role in improving the new-energy-carrying capacity of distribution networks. Existing planning models for SOPs and [...] Read more.

Intelligent soft open points (SOPs) and energy storage systems (ESSs) are effective ways to absorb distributed new energy in the spatial and temporal dimensions, and play an important role in improving the new-energy-carrying capacity of distribution networks. Existing planning models for SOPs and ESSs in distribution networks are often nonlinear and non-convex, and are usually transformed into a mixed-integer second-order cone optimization (MISOCP) model. However, this transformation often needs stringent relaxation conditions, and the solution speed and convergence performance of the model are poor. These disadvantages make traditional MISOCP models unsuitable for optimal planning for complex hybrid networks. To overcome these limitations, a joint planning method for AC/DC hybrid networks based on an improved DC power flow (IDCPF) algorithm is proposed in this paper. The proposed method transforms the original nonlinear model into an approximate linear model, improving the solution speed and accuracy of the model. The effectiveness of the proposed method is validated through case studies on an improved AC/DC 43-node network, which demonstrates the accuracy and numerical stability of the planning model. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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25 pages, 3345 KB

Open AccessArticle

Edge-Side Electricity-Carbon Coordinated Hybrid Trading Mechanism for Microgrid Cluster Flexibility

by Hualei Zou, Qiang Xing, Bitao Xiao, Xilong Xing, Andrew Yang Wu and Jiaqi Liu

Processes 2026, 14(1), 83; https://doi.org/10.3390/pr14010083 - 25 Dec 2025

Cited by 1 | Viewed by 1241

Abstract

High penetration of renewable energy sources (RES) in power systems introduces substantial source-load uncertainty and flexibility challenges, leading to misalignments between economic optimization and environmental sustainability. An edge-side electricity-carbon coordinated hybrid trading mechanism was proposed to enhance flexibility in microgrid clusters. A three-layer [...] Read more.

High penetration of renewable energy sources (RES) in power systems introduces substantial source-load uncertainty and flexibility challenges, leading to misalignments between economic optimization and environmental sustainability. An edge-side electricity-carbon coordinated hybrid trading mechanism was proposed to enhance flexibility in microgrid clusters. A three-layer time-varying carbon emission factor (CEF) model is developed to quantify negative emissions as tradable Chinese Certified Emission Reductions (CCERs). An endogenous economic equilibrium point enables dynamic switching between Incentive-Based Demand Response during high-carbon periods and Price-Based Demand Response during low-carbon periods, based on marginal profit comparisons. A Wasserstein distance-based distributionally robust CVaR (WDR-CVaR) strategy constructs a data-driven ambiguity set to optimize decisions under worst-case distributional shifts in edge-side data. Simulations on a modified IEEE 33-bus system show that the mechanism increases the Multi-Energy Aggregator’s (MEA) expected profit by 12.3%, reduces carbon emissions by 17.6%, with WDR-CVaR demonstrating superior out-of-sample performance compared to sample average approximation methods. The approach internalizes environmental values through carbon-electricity coupling and edge intelligence, providing a resilient framework for low-carbon distribution network operations. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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26 pages, 1419 KB

Open AccessArticle

Hybrid AC/DC Transmission Grid Planning Based on Improved Multi-Step Backtracking Reinforcement Learning

by Zhe Wang, Yuxin Dai, Wenxin Yang, Yunzhang Yang, Zhiqi Zhang, Yahan Hu, Jianquan Liao and Tianchi Wu

Processes 2026, 14(1), 11; https://doi.org/10.3390/pr14010011 - 19 Dec 2025

Cited by 2 | Viewed by 709

Abstract

Hybrid AC/DC transmission expansion planning must balance investment cost, supply reliability and AC/DC stability, which challenges conventional mathematical programming and heuristic methods. This paper proposes a multi-objective planning framework based on an improved multi-step backtracking α-Q(λ) reinforcement learning algorithm with eligibility traces and [...] Read more.

Hybrid AC/DC transmission expansion planning must balance investment cost, supply reliability and AC/DC stability, which challenges conventional mathematical programming and heuristic methods. This paper proposes a multi-objective planning framework based on an improved multi-step backtracking α-Q(λ) reinforcement learning algorithm with eligibility traces and an adaptive learning factor. A tri-objective model minimises annual economic cost, expected power shortage and a comprehensive electrical index that combines electrical betweenness, commutation-failure margin and effective short-circuit ratio. The mixed-integer planning problem is reformulated as an interactive learning process, where the state encodes candidate line construction decisions, the action builds or cancels lines, and the eligibility-trace matrix is used to quantify line importance. Case studies on the Garver-6 system, the IEEE 24-bus reliability test system and a 500 kV regional hybrid AC/DC grid show that, compared with classical Q-learning, the proposed method yields lower annual cost, reduced expected power shortage and improved AC/DC stability; in the 500 kV system, the expected annual power shortage is reduced from 70,810 MWh to 28,320 MWh. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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18 pages, 578 KB

Open AccessArticle

Physics-Constrained Graph Attention Networks for Distribution System State Estimation Under Sparse and Noisy Measurements

by Zijian Hu, Zeyu Zhang, Honghua Xu, Ye Ji and Suyang Zhou

Processes 2025, 13(12), 4055; https://doi.org/10.3390/pr13124055 - 15 Dec 2025

Cited by 2 | Viewed by 1292

Abstract

Accurate state estimation is essential for the real-time operation and control of modern distribution systems characterized by high renewable energy penetration, bidirectional power flows, and volatile loads. Conventional model-driven approaches such as the Weighted Least Squares (WLS) exhibit limited robustness under noisy and [...] Read more.

Accurate state estimation is essential for the real-time operation and control of modern distribution systems characterized by high renewable energy penetration, bidirectional power flows, and volatile loads. Conventional model-driven approaches such as the Weighted Least Squares (WLS) exhibit limited robustness under noisy and sparse measurements, while existing data-driven methods often neglect critical physical constraints inherent to power systems. To address these limitations, this paper proposes a physics-constrained Graph Attention Network (GAT) framework for distribution system state estimation (DSSE) that synergistically integrates data-driven learning with physical domain knowledge. The proposed method comprises three key components: (1) a Gaussian Mixture Model (GMM)-based data augmentation strategy that captures the stochastic characteristics of loads and distributed generation to generate synthetic samples consistent with actual operating distributions; (2) a GAT-based feature extractor with topology-aware admittance matrix embedding that effectively learns spatial dependencies and structural relationships among network nodes; and (3) a physics-constrained loss function that incorporates nodal power and voltage limit penalties to enforce operational feasibility. Comprehensive evaluations on the real-world 141-bus test system demonstrate that the proposed method achieves mean absolute error (MAE) reductions of 52.4% and 45.5% for voltage magnitude and angle estimation, respectively, compared to conventional Graph Convolutional Network (GCN)-based approaches. These results validate the superior accuracy, robustness, and adaptability of the proposed framework under challenging measurement conditions. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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25 pages, 2590 KB

Open AccessArticle

Enhancing Distribution Network Flexibility via Adjustable Carbon Emission Factors and Negative-Carbon Incentive Mechanism

by Hualei Zou, Qiang Xing, Hao Fu, Tengfei Zhang, Yu Chen and Jian Zhu

Processes 2025, 13(12), 4023; https://doi.org/10.3390/pr13124023 - 12 Dec 2025

Cited by 1 | Viewed by 865

Abstract

With increasing penetration of distributed renewable energy sources (RES) in distribution networks, spatiotemporal mismatches arise between static time-of-use (TOU) pricing and real-time carbon emission factors. This misalignment hinders demand-side flexibility deployment, potentially increasing high-carbon-period consumption and impeding low-carbon operations. To address this, the [...] Read more.

With increasing penetration of distributed renewable energy sources (RES) in distribution networks, spatiotemporal mismatches arise between static time-of-use (TOU) pricing and real-time carbon emission factors. This misalignment hinders demand-side flexibility deployment, potentially increasing high-carbon-period consumption and impeding low-carbon operations. To address this, the paper proposes an adjustable carbon emission factor (ADCEF) which decouples electricity from carbon liability using storage. The strategy leverages energy storage for carbon responsibility time-shifting to build a dynamic ADCEF model, introducing a negative-carbon incentive mechanism which quantifies the value of surplus renewables. A revenue feedback mechanism couples ADCEF with electricity prices, forming dynamic price troughs during high-RES periods to guide flexible resources toward coordinated peak shaving, valley filling, and low-carbon responses. Validated on a modified IEEE 33-bus system across multiple scenarios, the strategy shifts resources to carbon-negative periods, achieving 100% on-site excess RES utilization in high-penetration scenarios and, compared to traditional TOU approaches, a 27.9% emission reduction and 8.3% revenue increase. Full article

(This article belongs to the Special Issue Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement)

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