Journal of Modern Power Systems and Clean Energy

ISSN 2196-5625 CN 32-1884/TK

  • Volume 14,Issue 4,2026 Table of Contents
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    • >Featured Theme: Cyber Security and Privacy Protection for Virtual Power Plant Operation
    • Cybersecurity in Virtual Power Plants: A Review of Theoretical Framework, Risk Analysis, and Defense Technologies

      2026, 14(4):1151-1171. DOI: 10.35833/MPCE.2026.000042

      Abstract () HTML () PDF 973.54 K () Comment (0) Favorites

      Abstract:Virtual power plants (VPPs) can participate in electricity market trading by aggregating distributed energy resources, thereby providing flexible regulation services to the power system. However, the interaction between VPPs and the power system involves high-frequency and multi-party data exchange, posing significant cybersecurity risks. To ensure the cybersecurity of VPPs throughout the entire interaction process, this paper first analyzes the intrinsic attributes of VPPs, identifying three key characteristics: aggregation, interaction, and regulation. Based on this, it integrates these attributes with confidentiality, integrity, and availability triad to construct a cybersecurity theoretical framework for VPPs. Second, this paper outlines the business processes, data interactions, and communication architecture of VPPs. Then, a risk analysis of potential cyberattacks is performed, detailing their injection points, propagation paths, and potential impacts of typical cyberattacks. Third, the core application mechanisms and use cases of key cybersecurity defense technologies are summarized. These technologies are applicable to interactions between VPP and power systems across different stages, including data anonymization, encryption, privacy-preserving computation, access control, and blockchain. Finally, an analysis of the current status, challenges, and prospects of artificial intelligence (AI)-based cybersecurity technologies is presented, which provides support for constructing a secure and reliable cybersecurity defense system for VPPs.

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    • Value-based Data Governance and Security Protection for Virtual Power Plants Aggregated by Demand-side Flexible Loads

      2026, 14(4):1172-1184. DOI: 10.35833/MPCE.2025.000787

      Abstract () HTML () PDF 32.15 K () Comment (0) Favorites

      Abstract:Virtual power plants (VPPs) aggregated by demand-side flexible loads have become a key mechanism for balancing supply and demand in power systems. However, compared with conventional power plants, VPPs generate vast and heterogeneous datasets that are challenging to manage and protect effectively. Existing solutions often fail to unlock the full value of these data while imposing excessive security costs. This paper proposes a value-based data governance and security protection framework tailored for VPPs aggregated by demand-side flexible loads. Within this framework, a real-time data value assessment model is developed to dynamically assess the value of demand-side flexible load data. Furthermore, a fine-grained data management and protection strategy is introduced to enable differentiated governance and security measures. These measures are applied across different stages of the data life cycle according to the assessed data value levels. Numerical results demonstrate that the proposed framework enhances both data protection and operational performance while reducing security costs. Moreover, it promotes data circulation and value creation, and supports the sustainable and intelligent transformation of modern power systems.

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    • A Blockchain-enabled Cyber-resilient Trading Framework for Virtual Power Plants

      2026, 14(4):1185-1197. DOI: 10.35833/MPCE.2025.000244

      Abstract () HTML () PDF 1.63 M () Comment (0) Favorites

      Abstract:The rapid expansion of distributed energy resources (DERs) has driven the emergence of virtual power plants (VPPs) as decentralized energy trading platforms that enhance grid flexibility and market efficiency. However, the increasing reliance on digital infrastructure has exposed VPP transactions to cyber-threats such as double-spending attack, Sybil attack, smart contract tampering, and malicious data injection attack, undermining transaction integrity and market stability. Traditional cybersecurity mechanisms, which often rely on centralized verification, are vulnerable to single points of failure and lack adaptive defense strategies. To address these challenges, this paper proposes a blockchain-enabled cyber-resilient trading framework that integrates game-theoretic smart contract optimization, Byzantine fault tolerance (BFT) consensus mechanisms, and zero-knowledge proof (ZKP) authentication to enhance cybersecurity, efficiency, and privacy in VPP transactions. The proposed framework leverages a multi-layered cybersecurity approach where game-theoretic modeling ensures optimal cybersecurity investment by balancing transaction efficiency and cybersecurity costs. A Stackelberg game modeling models the interactions among prosumers, VPP aggregators, and cyber attackers, allowing the system to allocate cybersecurity resources strategically. ZKP authentication ensures that transactions are validated without exposing sensitive trading information, mitigating privacy risks while maintaining transparency. To enhance resilience, a reinforcement learning-based adaptive defense mechanism continuously optimizes cybersecurity policies against evolving cyber-threats, improving attack detection and mitigation efficiency. The proposed framework incorporates multi-signature validation and BFT consensus mechanisms to prevent unauthorized modifications, while smart contracts autonomously execute transactions under predefined cybersecurity policies.

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    • Day-ahead Pricing Strategy for Virtual Power Plants Considering Privacy Protection of User Data

      2026, 14(4):1198-1209. DOI: 10.35833/MPCE.2025.000971

      Abstract () HTML () PDF 853.33 K () Comment (0) Favorites

      Abstract:As an advanced aggregation and control technology for multi-type source-load resources, virtual power plant (VPP) enables intelligent interconnection and coordinated optimization of distributed load resources. This paper proposes a day-ahead pricing strategy for VPPs considering privacy protection of user data. First, a day-ahead pricing model for VPP is constructed, which considers historical demand response (DR) contributions of users to enhance fairness in the pricing process. The asynchronous advantage actor-critic (A3C) algorithm is adopted to solve this model and optimize pricing decisions. Furthermore, an encrypted horizontal federated learning (HFL) method is proposed for model training, which is based on improved weighted federated averaging algorithm and aims to mitigate data silos and protect privacy of user data across different regions. Instead of directly transmitting user data during training, partially homomorphic encryption (PHE) scheme is applied to encrypt exchanged model parameters, thereby reducing the risk of privacy leakage. Case studies validate that the proposed pricing strategy can enhance the fairness of multi-user regulation decisions and improve the performance of VPPs in day-ahead DR while ensuring the security of user data.

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    • >Review
    • Net Load Forecasting for Renewable Energy Integrated Power Systems: A Critical Review

      2026, 14(4):1210-1227. DOI: 10.35833/MPCE.2025.000940

      Abstract () HTML () PDF 858.22 K () Comment (0) Favorites

      Abstract:Net load (NL) refers to the difference between gross demand and variable renewable energy (RE) generation. As the integration of RE continues to grow, the variability and uncertainty of power systems increase, creating significant challenges for power system operators due to the intermittent behavior of RE sources. NL forecasting (NLF) has become crucial to maintaining the reliable and secure operation of power systems. This paper critically reviews the state-of-the-art NLF models in RE-integrated power systems, with a particular focus on emerging techniques such as Transformer models and generative artificial intelligence (Gen-AI) models. This paper systematically explores and analyses various data preprocessing, feature engineering (feature selection and extraction), and hyperparameter tuning methods as well as forecasting engines used in NLF. Furthermore, this paper categorizes the NLF models with corresponding strengths and challenges. In addition, an assessment of the interpretability, scalability, and applicability of NLF models is presented, highlighting their performance under varying levels of RE penetration. This paper also outlines challenges for NLF, e.g., the quality of data and the spatial and temporal scales. Finally, the future research directions are outlined based on the identified gaps in NLF.

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    • A Review of Optimal Scheduling and Distributed Cooperative Control for Smart Grids Integrated with Electric Vehicles

      2026, 14(4):1228-1245. DOI: 10.35833/MPCE.2025.000176

      Abstract () HTML () PDF 1.59 M () Comment (0) Favorites

      Abstract:The technological development of smart grids (SGs) has recently gained increased momentum due to large-scale integration of renewable energy sources (e.g., wind and photovoltaic power) and highly variable loads, including electric vehicles (EVs) along with the deepened decarbonization in power and transport systems as two major greenhouse gas-emitting sectors worldwide. With the development of SGs, fruitful achievements in optimal scheduling and distributed cooperative control have been made. However, a comprehensive survey of these methods covering the low-carbon, economy, and cybersecurity metrics is still missing. This paper bridges the gap with the aim of providing an in-depth overview of optimal scheduling and distributed cooperative control from the whole system perspective within the SG framework. First, the fundamental mathematical models of optimal scheduling for low-carbon, economy, and cybersecurity operations are reviewed, the corresponding solution methods are summarized, and the cooperative optimization and scheduling methods for SGs integrated with EVs are specifically analyzed. Second, the performances of centralized and distributed cooperative control methods are compared, and two popular distributed cooperative control frameworks, namely centralized-distributed and autonomous-distribute frameworks, are further discussed comprehensively. Third, typical real-world applications of optimal scheduling and distributed cooperative control are analyzed. Finally, the trends and challenges of optimal scheduling and distributed cooperative control for effectively integrating EVs in SGs are prospected.

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    • >Original Paper
    • Control-level Sub-synchronous Oscillation Source Identification for IBRs-dominated Power Systems Based on Initial Instantaneous Power Characteristics

      2026, 14(4):1246-1258. DOI: 10.35833/MPCE.2025.000464

      Abstract () HTML () PDF 2.08 M () Comment (0) Favorites

      Abstract:Sub-synchronous oscillations (SSOs) originating from inverter-based resources (IBRs), which can be specifically induced by different controls within IBRs, have become a significant challenge to the stability of power system. Identifying the specific control responsible for the oscillation is crucial for effective oscillation mitigation. However, the coupling of multi-frequency disturbance terms, along with the complexities introduced by nonlinear elements, makes it difficult to isolate the impact of individual control. To address this issue, this paper proposes a control-level SSO source identification method for IBRs-dominated power systems based on initial instantaneous power characteristics. First, the expressions of instantaneous power during SSOs induced by different controls are derived for grid-following (GFL)-IBRs and grid-forming (GFM)-IBRs. The causes of current saturation triggering are revealed, and the coupling effects introduced by nonlinear elements are examined. Then, the initial instantaneous power characteristics of grid-side converter (GSC)-control-induced oscillations (GCIOs) and synchronization-control-induced oscillations (SCIOs) are analyzed, by comparing cases where the saturation limit is reached and not reached. The proposed method incorporates the dynamic characteristics of IBR controls, and can identify the SSO source using measurement data at the IBR port. Finally, the effectiveness of the proposed method in various SSO scenarios is validated through real-time simulations. Comparisons with existing methods demonstrate that the proposed method achieves higher identification accuracy.

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    • Multiscale Energy Coordination of Integrated Thermal Power-Energy Storage System for Enhanced Primary Frequency Regulation

      2026, 14(4):1259-1271. DOI: 10.35833/MPCE.2025.000607

      Abstract () HTML () PDF 3.99 M () Comment (0) Favorites

      Abstract:The increasing integration of renewable energy sources weakens system frequency security, requiring enhanced primary frequency regulation (PFR) from conventional thermal power units (TPUs). In this case, integrating energy storage system (ESS) with TPUs offers a promising solution. However, most existing methods primarily focus on turbine dynamics while overlooking multiscale coordination among ESS, turbine, and boiler, thereby limiting sustained power support and safe operation of TPUs. To this end, this paper firstly analyzes the multiscale energy dynamics of TPUs under power disturbances, revealing that insufficient boiler thermal storage can cause secondary frequency dips (SFDs). An analytical energy balance equation is then established to quantify the ESS energy requirement for compensating thermal storage. Based on this, a novel multiscale energy coordination method for the integrated thermal power energy storage system (TPESS) is developed, including three dedicated controls: a deviation-based power control (DPC) for ESS, a coordinated energy allocation (CEA) between thermal storage and ESS, and a fuel-assisted restoration (FAR) for state of charge (SOC). This method enables the ESS to take the leading role in PFR while simultaneously coordinating with the boiler thermal storage and fuel systems to ensure safe operation and state recovery. Simulation in DIgSILENT/PowerFactory validates the effectiveness of the proposed method in enhancing system frequency security and boiler safety.

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    • Corrective N-k Security-constrained Unit Commitment Using Lossy Shift Factors and Fictitious Injections

      2026, 14(4):1272-1283. DOI: 10.35833/MPCE.2025.000430

      Abstract () HTML () PDF 672.73 K () Comment (0) Favorites

      Abstract:Power systems worldwide are increasingly experiencing the simultaneous failure of multiple components due to severe weather conditions, which are becoming more frequent and intense. This consequently triggers growing interest in more stringent security standards. Indeed, electricity markets are moving toward explicitly including generator outages within auction models seeking the most economical and reliable generation scheduling and dispatch. Within this context, a corrective N-k security-constrained unit commitment model is proposed to address the need for tighter security standards. As a major distinctive feature, the proposed model jointly considers multiple out-of-service generators and lines, corrective actions, and transmission line losses. Moreover, unlike previous studies, lossy shift factors are used to represent the effect of the lossy transmission network while accurately characterizing transmission line losses by a binary-variable-based piecewise linear approximation. Additionally, line outages are incorporated by modeling fictitious injections of active power. The proposed model using lossy shift factors and fictitious injections is cast as an instance of mixed-integer linear programming. The solution of the resulting mathematical problem allows co-optimizing energy and reserves to accommodate the power fluctuations due to the component outages under consideration. Numerical experience is reported using three standard benchmarks comprising 14, 118, and 500 buses.

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    • A Data-driven and Deep Learning-based Method for Power System Operating Mode Identification

      2026, 14(4):1284-1296. DOI: 10.35833/MPCE.2025.000634

      Abstract () HTML () PDF 1.54 M () Comment (0) Favorites

      Abstract:Efficient and accurate analysis for power system operating mode identification is crucial for handling the operation, planning, and stability analysis of future power systems. This paper proposes a data-driven and deep learning-based method for power system operating mode identification, while also addressing the needs for identifying future operating modes. Firstly, an operating mode analysis method is developed based on adaptive threshold affinity propagation (AP) clustering with dynamic time warping (DTW), which incorporates historical load sequences and employs a modified distance function and adaptive thresholds for clustering. Secondly, a parallel temporal fusion network (PTFN) model with temporal feature projection is proposed to address load uncertainty. Finally, based on the results of historical operating mode analysis and future load forecasting, a Shapley additive explanation with parallel temporal convolution network and the squeeze-excitation mechanism (SHAP-PTCN-SE) is proposed for identifying future operating modes. Numerical examples demonstrate the efficiency and accuracy of the proposed data-driven and deep learning-based method in identifying future operating modes, providing guidance for system monitoring and protection.

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    • Multi-turbine Cooperative Frequency Regulation Control for Wind Farms Considering Torque-limited Inertial Control Power Characteristics

      2026, 14(4):1297-1307. DOI: 10.35833/MPCE.2025.000547

      Abstract () HTML () PDF 901.57 K () Comment (0) Favorites

      Abstract:Torque-limited inertial control (TLIC) offers advantages of stabilizing wind turbine (WT) operation and mitigating secondary frequency dip. When large-scale wind farm (WF) clusters simultaneously employ TLIC to provide power support, unnecessary frequency recoil (FR) phenomenon may occur, persistently degrading the frequency regulation performance. To address this issue, the paper analyzes the frequency response characteristic under TLIC method, and derives the conditions for FR under simultaneous and immediate support and simultaneous and delayed support, with the latter exhibiting more pronounced FR effects. The root cause of FR is identified as excessive power increments. Hence, the multi-turbine cooperative frequency regulation control method for WFs considering the TLIC power characteristics is proposed. By sequentially activating TLIC among WTs, the excessive power increment from simultaneous support is mitigated, and the gradual power reduction of the engaged WTs can be compensated. Experimental validation is conducted based on the test bench of wind-integrated power system, which demonstrates that the proposed method effectively avoids FR and further enhances the frequency nadir.

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    • Grid-friendly Coordinated Robust Control of Multiple Wind Farms for System Frequency Support and Damping Enhancement

      2026, 14(4):1308-1320. DOI: 10.35833/MPCE.2025.000108

      Abstract () HTML () PDF 1.75 M () Comment (0) Favorites

      Abstract:Additional control strategies are often incorporated into inverter-based renewable energy sources to enhance the stability of power systems, which introduce frequency response and damping controls that affect the small-signal stability of the system. To address the issues of diminished frequency support capability and damping levels in power systems following the integration of multiple wind farms (WFs), this study investigates the interaction between integrated inertia control and power oscillation damping control. We then propose a grid-friendly coordinated robust control of multiple WFs to simultaneously provide system frequency support and damping enhancement. First, the coupling characteristics of the additional control loops in the WFs are analyzed using a multi-machine damping torque analysis. Then, based on the principles of optimal frequency response ability and optimal damping support ability of WFs, a coordinated robust control model of multiple WFs is established to maximize frequency offset improvements and maximize the minimum damping ratio of dominant oscillation modes. Finally, a multi-objective model-solving algorithm based on eigenvalue sensitivity analysis is proposed to determine the optimal control coefficients. Simulation results demonstrate the effectiveness of the proposed control for WFs in system frequency support and damping enhancement.

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    • Asynchronous Hierarchical Volt/var Control for Offshore Wind Farms

      2026, 14(4):1321-1334. DOI: 10.35833/MPCE.2025.000141

      Abstract () HTML () PDF 1.17 M () Comment (0) Favorites

      Abstract:Utilizing the reactive power (var) capability of wind turbines (WTs) has become the primary method for increasing var reserves in offshore wind farms. However, current methods place an unbearable burden on outdated equipment, which requires frequent communication. Catering to this problem, an asynchronous hierarchical voltage/var (volt/var) control (AHVC) method is proposed, which is constrained by the original communication capability and topology of collector grid, and embedded in a master-slave multi-agent system with an asynchronous hierarchical control scheme. The proposed AHVC method is built on the bilinear optimal power flow (Bilinear-OPF) model with a parallel alternating direction method of multipliers (ADMM) algorithm. It resolves voltage distortion issues in high-capacitance grids by ensuring more precise var targeting across the grid, then the var burden on the static synchronous compensator (STATCOM) is reduced. Additionally, the volt/var sensitivity-based Mahalanobis norm hyperparameter setting method ensures local compensation of var sources. The proposed AHVC method achieves rapid convergence and reliable performance amid typical load volatilities of WTs. Simulation results verify the significant improvement of accuracy and voltage stability, even under challenging communication conditions.

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    • High-proportion Reactive Power Compensation Control for Delta-connected High-voltage Transformerless Battery Energy Storage System via Optimal Zero-sequence Current Injection

      2026, 14(4):1335-1347. DOI: 10.35833/MPCE.2025.000516

      Abstract () HTML () PDF 1.89 M () Comment (0) Favorites

      Abstract:The structural configuration of delta-connected high-voltage transformerless battery energy storage system (D-HVT-BESS) inherently introduces second-order ripple currents (SORCs) into the battery cells. Under low power factor conditions, the SORCs exhibit frequent zero-crossing, which accelerates battery aging and compromises the accuracy of state monitoring. Therefore, a high-proportion reactive power compensation control method for D-HVT-BESS via optimal zero-sequence current injection is proposed. The key to the proposed method is to use zero-sequence current to adjust the reactive-to-active power ratio of each phase leg. This adjustment enhances the power factor per phase, thereby eliminating the zero-crossing of SORCs. Furthermore, an optimization model is formulated to minimize the system power loss induced by zero-sequence current. The optimization model achieves this by optimizing the amplitude and phase angle of zero-sequence current. Additionally, to mitigate the inter-phase state of charge (SOC) imbalance caused by the zero-sequence current, an inter-phase SOC balancing control strategy based on an absolute phase selector is developed, enabling real-time optimization of the absolute phase of zero-sequence current to achieve dynamic SOC equalization among phases. Finally, a 380 V/100 kW/50 kWh experimental prototype is constructed for validation. Experimental results verify the effectiveness and operational feasibility of the proposed method.

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    • Spatio-temporal Hybrid Graph-Transformer Model for High-fidelity Renewable Energy Forecasting

      2026, 14(4):1348-1360. DOI: 10.35833/MPCE.2025.000504

      Abstract () HTML () PDF 1.01 M () Comment (0) Favorites

      Abstract:Accurate wind and solar power forecasting is crucial for grid stability and renewable energy integration, especially in island like Jeju Island, Republic of Korea. This paper tackles challenges such as nonlinear patterns, spatial interdependencies, and resource variability. Current models are limited because they are resource specific, treat spatial and temporal dependencies separately, and lack dynamic inter-site relationship modeling, which are essential in dispersed systems. To overcome these limitations, we propose a spatio-temporal hybrid graph-Transformer (ST-HGT) model for high-fidelity renewable energy forecasting, which combines graph attention networks (GATs), temporal convolutional networks (TCNs), neural basis expansion analysis for interpretable time-series forecasting (N-BEATS), Transformer, and Informer, within a modular architecture. The proposed ST-HGT model captures spatio-temporal dynamics by learning inter-site correlations from weather and power data via a dynamic graph and employing complementary temporal modules to model local features, long-range dependencies, and complex patterns. The proposed ST-HGT model is trained and evaluated independently for wind and solar power forecasting, using real-world datasets from multiple stations across Jeju Island. The results show that the proposed ST-HGT model markedly surpasses state-of-the-art baselines, including Informer, temporal fusion Transformer (TFT), N-BEATS, and recurrent networks. For solar power forecasting, the proposed ST-HGT model achieves a root mean square error (RMSE) of 21.71 kWh and a coefficient of determination R² of 0.999, with an improvement of more than 96.6% in RMSE relative to the best baseline model. For wind power forecasting, the proposed ST-HGT model achieves an RMSE of 853 kWh and an R² of 0.99, outperforming all baselines, which have RMSEs exceeding 65000 kWh.

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    • Adaptive Robust Optimization for Operation of Active Distribution Networks in Real-time Energy Markets

      2026, 14(4):1361-1373. DOI: 10.35833/MPCE.2025.000481

      Abstract () HTML () PDF 728.45 K () Comment (0) Favorites

      Abstract:Energy management system (EMS) and volt-var optimization (VVO) programs are jointly employed to achieve the efficient operation of active distribution networks (ADNs). However, current studies often overlook that the operation of ADNs is coupled with trading energy in real-time (RT) energy markets. To fill this gap, this paper develops an adaptive robust optimization (ARO) model of ADNs in RT energy markets. The studied ADN consists of photovoltaic (PV) units, electric vehicle (EV) charging stations, and flexible demands interconnected through a medium-voltage distribution network. Through the proposed model, the integrated EMS and VVO programs can decide to offer energy in the hourly RT energy market, schedule flexible demands, and adjust slow-acting devices (e.g., on-load tap changers and capacitors), while anticipating the operation conditions of the ADN under uncertain prices, charging power level of EVs, and available PV power generation through the uncertainty sets. Once the market outcomes are known, the integrated EMS and VVO programs dispatch the fast-acting devices of PV units and EV charging stations. The results of a realistic case study indicate that prioritizing the reduction of voltage violations leads to lower energy trading in the RT energy market and a decrease in profit.

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    • Tractable Modeling of Decision-dependent Customer Interruption Cost and Cold Load Pickup for Optimizing Power Distribution System Restoration

      2026, 14(4):1374-1386. DOI: 10.35833/MPCE.2025.000213

      Abstract () HTML () PDF 1.10 M () Comment (0) Favorites

      Abstract:Developing optimized restoration strategies for power distribution systems (PDSs) is critical to enhancing resilience. Prior knowledge of customer interruption cost (CIC) and load restoration behaviors, particularly cold load pickup (CLPU), is essential for effective decision-making. However, both CIC and CLPU are reciprocally influenced by the realized customer interruption duration (CID), making them decision-dependent and challenging to model, especially with limited understanding of underlying physical mechanisms. This study proposes a tractable modeling approach of decision-dependent CIC and CLPU for optimizing power distribution system restoration to capture the varying patterns of both CIC and CLPU with CID, i.e., patterns derived from data that reflect observable surface-level correlations rather than underlying mechanisms, thereby enabling practical surrogate modeling of decision-dependent factors. Specifically, quadratic functions are employed to model the increasing rate of CIC with respect to CID according to data fitting results. For CLPU, several defining characteristics are extracted and modeled in a piecewise linear form relative to CID, from which the actual restored load accounting for CLPU is subsequently reconstructed. Building on these models, a PDS restoration framework is developed, incorporating mobile energy storage systems (MESSs) and network reconfiguration strategies. Case studies validate the effectiveness of the proposed approach and highlight the unique potential of MESS in accelerating CLPU-related restoration.

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    • Polytope-based Aggregation Method for User-side Flexible Energy Resources to Improve Flexibility of Active Distribution Networks

      2026, 14(4):1387-1398. DOI: 10.35833/MPCE.2025.000776

      Abstract () HTML () PDF 1.03 M () Comment (0) Favorites

      Abstract:Improving the flexibility of active distribution networks (ADNs) enhances the reliability and economic performance of regional power systems. Common user-side flexible energy resources (FERs), which are numerous but individually limited in capacity, can be aggregated to participate in ADN operations. To accurately and efficiently aggregate heterogeneous user-side FERs, this paper proposes a novel polytope-based aggregation method to construct the aggregated feasible region, which is integrated into a coordinated operation model for ADNs. The proposed method employs an inner approximation using affine transformation to better capture the feasible regions of individual FERs. In addition, a distributionally robust chance-constrained (DRCC) model is integrated to address parameter uncertainties in FERs, and a rolling mechanism is applied to intraday operations for the rolling update of the aggregated feasible region. Finally, a case study of a specific ADN in Northwest China validates the effectiveness of the proposed method and the corresponding improvement in flexibility. The results indicate that the proposed coordinated operation model effectively improves the flexibility of ADNs, and the proposed method reduces the computational burden without compromising economic benefits.

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    • Three-stage Distributionally Robust Optimization Planning of Island Microgrid Cluster Considering Marine Environmental Uncertainties

      2026, 14(4):1399-1412. DOI: 10.35833/MPCE.2025.000600

      Abstract () HTML () PDF 2.51 M () Comment (0) Favorites

      Abstract:In order to fully utilize the energy resources of different offshore islands and improve the power reliability, establishing island microgrid (IMG) clusters has become a promising way for marine energy systems. However, the relatively harsh and variable weather condition poses challenges to the planning of IMGs. This paper proposes a three-stage distributionally robust optimization (DRO) planning model to configure IMG clusters considering marine environmental uncertainties. Firstly, an energy management framework for IMG clusters is established, which includes diesel generator, renewable energy generation, and fixed battery energy storage as the island energy supply components, and utilizes the submarine cables (SCs) as well as mobile energy storage vessels (MESVs) as the energy interconnections among different islands. Then, the ambiguity set for marine environmental uncertainties, which include the wind speed, solar irradiance, ocean current, and wave, is constructed based on Wasserstein distance. On this basis, the proposed planning model is established to configure island energy supply and link components. Specifically, the first stage determines the configuration of SCs and the capacity of energy storage systems and MESVs. The second stage determines the operational decisions and the third stage solves the real-time power dispatch of IMGs. Finally, the two-layer column constraint generation algorithm is utilized to solve the proposed planning model. A realistic island cluster in the South China Sea is selected for case study. The results show that the proposed planning model can greatly enhance the power reliability and reduce 30.8% operational costs of the IMG. In a real typhoon scenario, the expected energy not supplied (EENS) can be reduced by 59.3% through the adoption of the proposed planning model.

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    • Emergency Power Supply Strategy for Multi-microgrids Based on Improved Finite-time Consensus Algorithm

      2026, 14(4):1413-1426. DOI: 10.35833/MPCE.2025.000458

      Abstract () HTML () PDF 3.08 M () Comment (0) Favorites

      Abstract:Islanded multi-microgrids (MMGs) can provide reliable emergency power supply during extreme events. However, under complex operating conditions and disturbances, the effectiveness of this capability depends critically on the design of power supply strategies and the dynamic response performance of power system. To address this challenge, this paper proposes an emergency power supply strategy for MMGs based on improved finite-time consensus algorithm. The proposed strategy achieves frequency and voltage regulation, day-ahead preventive dispatch, and intra-day emergency control through consensus cooperation among agents. The day-ahead preventive dispatch comprises the optimization of distributed generator (DG) outputs at the microgrid (MG) level and power coordination at the MMG level, achieving inter-MG coordination while respecting the autonomy of individual MGs. In the presence of any disturbances, the intra-day emergency control adjusts DG outputs in real time according to their respective participation factors to maintain the scheduled power exchanges among MGs, thus enhancing the robustness of the proposed strategy. Furthermore, the improved finite-time consensus algorithm significantly accelerates the convergence speed of the solution. Case studies based on an MMG simulation model are conducted to verify the effectiveness and superiority of the proposed strategy.

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    • Distributed Power Management of Off-grid DC Fast Charging Station Integrated with Multi-microgrid System Under Uncertainty and Outage Conditions

      2026, 14(4):1427-1438. DOI: 10.35833/MPCE.2025.000660

      Abstract () HTML () PDF 1.30 M () Comment (0) Favorites

      Abstract:Numerous studies nowadays have examined direct current fast charging (DCFC) stations equipped with distributed generations and storage devices or integrated with microgrid (MG) systems. However, none have proposed effective power management for off-grid DCFC stations integrated with multi-microgrid (MMG) system. In this paper, innovative distributed power management schemes (DPMSs) for off-grid DCFC station integrated with MMG system (DCFC-MMG) under uncertainty and outage conditions are proposed using distributed control systems (DCSs). The DCFC station is equipped with a central battery unit (CBU) and four charging locations (CLs). The MMG comprises three renewable MGs, which can meet their own energy demands of the power grid independently and provide fast charging for electric vehicles (EVs). Communication among MGs, CLs, and the CBU occurs through distributed interactions. Moreover, the MGs not only provide proper support from DCFC stations during CBU outage considering generation uncertainty and demand fluctuations, but also mutually support each other through microgrid-to-microgrid (MG2MG) interactions under critical conditions such as the outage of any MG batteries. Vehicle-to-vehicle (V2V) and vehicle-to-microgrid (V2MG) capabilities have also been designed to address situations where the MG batteries are simultaneously disconnected. Nonlinear time-domain simulation performed in the MATLAB/Simulink environment demonstrates that the proposed DPMSs for off-grid DCFC-MMG perform effectively under various uncertainty and outage conditions.

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    • Distributed Model Predictive Control Strategy Based on Battery State and Degradation Awareness for V2G Frequency Response in Charging Stations

      2026, 14(4):1439-1450. DOI: 10.35833/MPCE.2025.000759

      Abstract () HTML () PDF 956.29 K () Comment (0) Favorites

      Abstract:The lack of battery state and degradation awareness in electric vehicles (EVs) participating in vehicle-to-grid (V2G) frequency response (FR) can accelerate battery degradation and impair frequency support. To address this issue, we propose a distributed model predictive control (DMPC) strategy based on battery state and degradation awareness for V2G FR in charging stations (CSs), explicitly integrating battery state and degradation into the proposed strategy. First, a resistor-capacitor (RC) equivalent circuit model of batteries is integrated into the V2G FR. This allows the controller to capture internal battery states including state-of-charge and battery degradation rate. The model also monitors signals such as voltage and current, thereby enhancing both model fidelity and practical implementability. Second, an equivalent degradation model of batteries is embedded within the V2G FR, enabling the controller to jointly account for battery state and degradation while supporting V2G FR. Finally, a cross-scale hierarchical framework for V2G control strategy is developed to decouple and coordinate battery-level states and grid-level power dispatch, achieving hierarchical coordination across individual batteries and the CS. Simulation results demonstrate that the proposed DMPC strategy improves frequency regulation effectiveness, limits V2G FR tracking deviation, enhances battery operation safety and degradation preservation, and achieves more balanced V2G FR power allocation among EVs.

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    • Hierarchical Coordination Optimization Method of Isolated Electricity-hydrogen Microgrids with High Penetration of Renewable Energy Sources

      2026, 14(4):1451-1464. DOI: 10.35833/MPCE.2025.000303

      Abstract () HTML () PDF 1.20 M () Comment (0) Favorites

      Abstract:Renewable energy sources (RESs), particularly solar and wind energy, present a viable pathway for decarbonizing isolated microgrids (MGs). However, as the penetration of RESs increases, ensuring the optimal utilization of RESs while maintaining the system reliability poses significant challenges for isolated MGs. Therefore, a hierarchical coordination optimization method of the isolated electricity-hydrogen MG with high penetration of RESs is proposed to achieve low-carbon dispatching. The developed isolated electricity-hydrogen MG is an integrated system featuring hybrid battery-hydrogen energy storage, which encompasses three interconnected subsystems: an AC subsystem, a DC subsystem, and a hydrogen subsystem. The proposed method can be divided into two dispatch horizons: an annual horizon and a daily horizon. The annual horizon focuses on the inter-day energy dispatch, addressing hydrogen storage boundary conditions to solve seasonal energy mismatches. The daily horizon focuses on the day-ahead power dispatch to ensure the daily power balance of MG, taking into account the errors in annual estimated data. The effectiveness of the proposed method is validated through a series of case studies for an isolated electricity-hydrogen MG under varying penetrations of RESs and energy storage configurations. Simulation results show the promising potential of the proposed method in facilitating sustainable isolated electricity-hydrogen MGs.

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    • LLM-augmented Multi-agent System for Trading Behavior Modeling in Coupled Electricity-Carbon Markets

      2026, 14(4):1465-1478. DOI: 10.35833/MPCE.2025.000645

      Abstract () HTML () PDF 950.77 K () Comment (0) Favorites

      Abstract:The deep integration of electricity and carbon markets introduces new challenges for trading behavior modeling, driven by strategic diversity, adaptive agent behaviors, and bidirectional market feedback. Traditional optimization and game-theoretic formulations, which rely on fixed rationality assumptions and static behavioral structures, often fail to capture these dynamics with sufficient fidelity. This paper proposes a large language model (LLM)-augmented multi-agent system (MAS) framework for trading behavior modeling in coupled electricity- carbon markets, where LLMs act as cognitive agents capable of generating context-dependent strategies, interpreting market rules, and responding to evolving system states. The MAS provides a structured environment for interaction among heterogeneous agents, enabling more expressive, adaptive, and interpretable representations of cross-market behaviors. Case studies based on China’ s coupled electricity- carbon markets demonstrate that the proposed framework can reflect realistic bidding responses, emission-driven adjustments, and market feedback dynamics. This paper also identifies key challenges and outlines future directions including constraint-aware generation to ensure feasibility, structured reasoning and memory to enhance interpretability, and improved computational efficiency to enable scalable MAS deployment.

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    • Multi-agent Bi-level Game Model for Park- level Integrated Energy System Based on Electricity-Carbon Market Collaborative Decision-making Mechanism

      2026, 14(4):1479-1490. DOI: 10.35833/MPCE.2025.000463

      Abstract () HTML () PDF 1.15 M () Comment (0) Favorites

      Abstract:Effective coordination between electricity and carbon markets is critical for enabling energy-efficient decarbonization in integrated energy system. However, the inherent differences in trading products and timescales between two markets render independent electricity- carbon market mechanism invalid and target mismatch, particularly within multi-agent market environments. Hence, a multi-agent bi-level game model for park-level integrated energy system (PIES) is proposed in this paper, incorporating a novel electricity-carbon market collaborative decision-making mechanism. An equal-interval time discretization method is developed to reconcile the heterogeneity of discrete electricity market and continuous carbon market, enabling consistent timescale coordination. An improved alternating direction method of multipliers (ADMM) algorithm based on Peaceman-Rachford is adopted to achieve benefit allocation and rapid privacy-solving. Simulation results demonstrate the effectiveness of proposed multi-agent bi-level game model in balancing carbon reduction and economic efficiency, and enhancing the operation efficiency of multi-agent collaboration.

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    • Optimal Urban Multi-network Coordination Considering Hybrid Pricing Strategy for Electricity and Hydrogen Trading

      2026, 14(4):1491-1502. DOI: 10.35833/MPCE.2025.000147

      Abstract () HTML () PDF 649.22 K () Comment (0) Favorites

      Abstract:The growing demand for optimal urban multi-network coordination has intensified the interdependencies among urban transportation, energy systems, and carbon emissions, with integrated charging stations (ICSs) playing a pivotal role in this interconnected ecosystem. However, optimal coordination across these networks and hybrid pricing strategy for electricity and hydrogen trading remain significant challenges. This paper presents an optimal urban multi-network coordination framework, integrating the urban traffic network (UTN), power distribution network (PDN), urban hydrogen network (UHN), hydrogen supply chain (HSC), ICS, and carbon emission evaluation. The proposed framework aims to maximize regional social welfare, support low-carbon objectives, and optimize multi-network coordination through a two-layer iterative optimization process. Next, a hybrid pricing strategy for electricity and hydrogen trading is introduced, focusing on addressing urban safety constraints. This strategy employs peer-to-peer (P2P) trading for transactions between logistics operators and ICSs. Finally, simulation results on a IEEE 20-node UTN and IEEE 33-node PDN validate the efficiency and accuracy of the proposed framework, demonstrating improvements in multi-network coordination, reductions in traffic congestion and hydrogen transport risks, lower carbon emissions, and enhanced economic performance of both ICSs and central hydrogen production facility (CHPF).

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    • A Data-driven Multi-agent Framework for Electricity Market Simulation Using Practical and Heterogeneous Bidding Strategy Spaces

      2026, 14(4):1503-1514. DOI: 10.35833/MPCE.2025.000212

      Abstract () HTML () PDF 1.82 M () Comment (0) Favorites

      Abstract:Existing electricity market simulation research assumes that energy providers share theoretical and homogeneous strategy spaces. However, practical bidding strategies differ significantly from those based on theoretical simulation. The factors that determine energy providers’ bidding patterns are heterogeneous. Ignorance of practical and heterogeneous bidding strategy spaces distorts real market results. To fill the research gap, this paper proposes a data-driven multi-agent framework for electricity market simulation using practical and heterogeneous bidding strategy spaces. Firstly, a clustering algorithm is proposed for extracting practical and heterogeneous bidding strategy spaces from historical bidding strategies. The bidding strategy spaces are formed by the centers. Then, energy providers are modeled by agents with practical and heterogeneous strategy spaces in a multi-agent framework. Finally, the proximal policy optimization is implemented by agents to model the bidding behaviors in markets. Numerical results based on real data from the Australian Energy Market Operator show that market clearing results under practical and heterogeneous strategy spaces are closer to reality than those under theoretical and homogeneous strategy spaces.

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    • Vulnerability Identification for Urban Power Networks Under Malicious Attacks Considering Topology Completion Uncertainties

      2026, 14(4):1515-1526. DOI: 10.35833/MPCE.2024.000803

      Abstract () HTML () PDF 995.49 K () Comment (0) Favorites

      Abstract:Urban power network (UPN) topologies are partially observable due to invisible underground cables, leading to incomplete information under malicious attacks. To perform vulnerability identification for UPN under such attacks, it is of great importance to consider topology completion uncertainties in attack and defense strategies. To this end, this paper first proposes a UPN topology completion method, where a series of possible complete topologies associated with their corresponding probabilities are determined by means of Monte Carlo simulation and a knowledge-assisted hierarchical network partitioning algorithm, i.e., the improved SHRINK (I-SHRINK) algorithm. Subsequently, a bi-level stochastic optimization model is established to determine attack strategies by considering topology completion uncertainties, further identifying UPN vulnerability. The upper-level problem aims to maximize the expected load shedding risk, while the goal of lower-level problem is to minimize the total load shedding. Case studies are performed in a real UPN to verify the effectiveness and superiority of the UPN topology completion and vulnerability identification methods.

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    • Intrusion Detection and Mitigation System for Smart Inverters Based on Machine Learning and Environmental Sensors

      2026, 14(4):1527-1537. DOI: 10.35833/MPCE.2025.000713

      Abstract () HTML () PDF 618.39 K () Comment (0) Favorites

      Abstract:The rapid expansion of renewable energy deployment has accelerated the adoption of smart inverters in solar farms. However, their reliance on communication networks introduces cybersecurity vulnerabilities that make inverter measurements susceptible to manipulation. This paper presents an intrusion detection and mitigation system (IDMS) for smart inverters, which leverages machine learning algorithms and environmental sensor data to enhance data integrity and operational resilience. The proposed IDMS integrates the machine learning algorithms to combine a detection system with a mitigation system. The detection system integrates environmental sensor inputs with inverter measurements to accurately identify normal operating behavior and anomalous conditions in real time. To address the cumulative error challenges that arise during attacks, a prediction model based on long short-term memory (LSTM) and trained solely on environmental features is introduced in the mitigation system to reconstruct compromised voltage and current data, thereby preventing recursive cumulative error propagation and ensuring stable system operation. Case studies demonstrate that the proposed IDMS can promptly detect cyberattacks, replace compromised measurements with reliable estimates, and restore normal operation once attacks cease. Additional evaluations across varying data availability conditions in an open dataset confirm the robustness and scalability of the proposed IDMS, making it practical for diverse solar farm deployment environments.

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    • Poincaré-type Virtual Oscillator Control and Passivity-based Transient Stability Enhancement Method for Grid-forming Inverters

      2026, 14(4):1538-1548. DOI: 10.35833/MPCE.2025.000392

      Abstract () HTML () PDF 2.13 M () Comment (0) Favorites

      Abstract:To solve the limitations of existing virtual oscillator control (VOC), this paper presents the Poincaré-type VOC (PVOC) for grid-forming inverters and further provides a passivity-based transient stability enhancement method for PVOC. First, the core equation of PVOC is formulated based on the Poincaré bifurcation equation, and its advantages of steady droop characteristics and dynamic performances are analyzed. Second, a passivity-based control for PVOC (PBC-PVOC) is designed based on the energy damping and pumping method to enhance the system transient stability. The method of passivating the closed-loop system is illustrated, and the passivity conditions and parameter selections are analyzed in detail. Subsequently, a virtual impedance based current limiting method is presented for PBC-PVOC to effectively prevent the overcurrent under large disturbances. Finally, the time-domain simulation and experiments are carried out for the effectiveness validation under multiple operating conditions.

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