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Advances in Optimal Operation of Modern Power Systems for Flexibility...
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Advances in Optimal Operation of Modern Power Systems for Flexibility Enhancement

A special issue of Processes (ISSN 2227-9717). This special issue belongs to the section "Energy Systems".

Deadline for manuscript submissions: 20 May 2026 | Viewed by 3654

Special Issue Editors

Dr. Wennan Zhuang

E-Mail Website
Guest Editor
School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210023, China
Interests: flexibility enhancement; energy storage system; electricity–hydrogen–ammonia-coupled system; modeling, planning, and regulation of modern power system
Special Issues, Collections and Topics in MDPI journals
Dr. Xia Shen

E-Mail Website
Guest Editor
School of Renewable Energy, Hohai University, Nanjing 211100, China
Interests: microgrid transient-steady state coordinated control; control–protection integration analysis; power-to-hydrogen coupling system optimal control
Dr. Jiayong Li

E-Mail Website
Guest Editor
College of Electrical and Information Engineering, Hunan University, Changsha 410082, China
Interests: renewable energy-integrated distribution system optimal operation and control; modern distribution system digital simulation; distributed energy trading; application of big data and artificial intelligence in smart grid
Special Issues, Collections and Topics in MDPI journals
Dr. Guangsheng Pan

E-Mail Website
Guest Editor
School of Electrical Engineering, Southeast University, Nanjing 210096, China
Interests: modern power system; electric-hydrogen collaborative planning and operation optimization; low-carbon economy and energy policy

Special Issue Information

Dear Colleagues,

The increasing penetration of intermittent renewable energy sources and uncertainties in multiple loads have intensified flexibility requirements in the modern power system, characterized by integrated electricity, gas, heating, cooling, and hydrogen networks. Flexibility, defined as the system’s capability to maintain a supply–demand equilibrium and adapt to variabilities across multiple energy carriers and temporal scales, is essential for accommodating renewable intermittency and ensuring operational reliability. A wide array of flexibility resources is currently available, including multi-energy storage systems, demand response, and energy conversion technologies. However, developing refined modeling approaches for these flexible resources and effective collaborative scheduling and control strategies still poses challenges. Consequently, fully exploiting multi-energy flexibility to optimize both system operational efficiency and reliability remains a key research focus that demands global attention.

This Special Issue aims to cover innovative operation strategies in flexibility enhancement through advanced scheduling and adaptive control of multi-energy infrastructures. Suitable topics for this Special Issue include, but are not limited to, the following:

  • Multi-scale forecasting model of renewable energy and multi-energy load.
  • Modeling method of flexible resources in the modern power system.
  • Flexibility quantification and assessment methodology.
  • Data-driven scheduling strategy for flexibility enhancement.
  • Intelligent control method of distributed flexible resources.
  • Market mechanism for flexible service.

Dr. Wennan Zhuang
Dr. Xia Shen
Dr. Jiayong Li
Dr. Guangsheng Pan
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Processes is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • modern power system
  • flexibility enhancement
  • renewable energy integration
  • multi-energy coupling
  • data-driven optimization
  • distributed control
  • energy storage system
  • flexibility market

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Published Papers (7 papers)

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Research

21 pages, 2828 KB  
Article
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
Viewed by 290
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  
Article
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 326
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  
Article
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 336
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  
Article
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
Viewed by 437
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  
Article
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 1 | Viewed by 435
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  
Article
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
Viewed by 696
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  
Article
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
Viewed by 503
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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