This paper investigates the distributed secondary control of AC microgrids (MGs) with energy storage systems (ESSs) subject to hybrid cyber attacks, including false data injection (FDI) and denial-of-service (DoS) attacks. Different from the existing distributed resilient control methods under hybrid attacks, a novel distributed resilient control method is proposed, which can precisely compensate for the influence of FDI attacks and makes full use of the secure information from neighbours in the presence of DoS attacks. Specifically, a set of iterative observers is first proposed to accurately estimate FDI attacks. Besides, a distributed dynamic event-triggered mechanism (DETM) with open-loop estimation is introduced to further save the communication resources during DoS attacks. Based on the iterative observers and the DETM, a distributed resilient controller is designed to compensate for FDI attacks on secondary controllers and tolerate DoS attacks. The stability of the closed-loop MG system is proven by the Lyapunov theory, and Zeno behavior is excluded through proof by contradiction. Finally, the proposed resilient control method is implemented in MGs with ESSs, and its effectiveness under hybrid attacks is validated by experiments on the real-time simulator OPAL-RT.
The low-voltage Bi-DCDS is capable of accommodating the steadily increasing penetration of DC sources and loads, comparing with other distribution architectures. However, the three-conductor supply structure suffers voltage unbalance issue between positive and negative ports under load-unbalanced conditions. To address this issue, this paper proposes a coordinated voltage mitigation method for the low-voltage Bi-DCDS based on MLDC. The advantage of MLDC over conventional LDC in voltage regulation, and the key considerations in parameter selection of MLDC are analyzed. According to the analysis, a set of performance indices are developed to evaluate voltage regulation effectiveness, and converter power-sharing balance under multi-terminal operation. Based on the indices, a multi-objective optimization model for MLDC parameters is formulated, and a Pareto optimal solution selection method based on adaptive weighting of objective function values is presented. Case studies demonstrate that the proposed MLDC approach can suppresses load-side voltage unbalance and maintaining converter port voltage imbalance within prescribed limits simultaneously. The proposed optimization framework achieves a balanced trade-off among the considered performance indices.
Grid code compliance assessment of inverter-based resources (IBRs) is inefficient and error-prone in engineering applications due to the manual processing required for numerous test scenarios and the reliance on information in unstructured documents. A large language model (LLM) capable of synthesizing information from documents has the potential to accelerate the assessment process; however, it lacks an appropriate framework to perform the task effectively. This paper proposes a dual-agent framework with two self-correction loops to automatically generate power system dynamic simulations. The generation process consists of two LLM Agent parts: Agent I is responsible for receiving the request prompt from the user, then transferring the reasoning output into a specific operational list with required functions; Agent II generates code for the plan list by retrieving from a memory database, synthesizing new functions if needed, and persistently storing them for future use. Meanwhile, two correction loops are used to rectify the plan and code, respectively, based on error feedback during generation, ensuring correctness and seamless automation throughout the process. In the case study, the modified IEEE and user-defined systems are tested under varied user instructions to verify the workflow and generalizability. Ablation studies on the framework and comparative evaluations of state-of-the-art LLMs are also conducted, demonstrating that the proposed workflow generalizes dynamic model generation with high accuracy and efficiency.
Real-time estimation of grid impedance can provide key guidance for the online control in grid-following (GFL) inverter, yet it is very changing due to the fast response performance of GFL during dynamic stage. This paper first reveals that the detected frequency deviation during dynamic stage is the main reason for inaccuracy of grid impedance estimation. Then, a frequency immune model of grid impedance estimation is proposed, in which a square sum operation is performed to eliminate the frequency-related nonlinear information contained in the grid voltage. Based on the frequency immune model, a real-time grid impedance estimation method is proposed, and it can converge to the actual value of the parameters before the system reaches stability, and can maintain normal operation even if the grid frequency fluctuates. Finally, simulation and experimental results are given to verify the validity and feasibility of this method.
Distributed secondary control of a microgrid (MG) is essential for stable and effective operation, yet actuator faults can severely compromise its performance. In this paper, the fault-tolerant distributed secondary control problem of AC MGs under hybrid actuator faults, including bias fault, partial loss of effectiveness (PLOE) fault, and outage fault, is investigated. To solve this problem, a data-driven fault-tolerant method is proposed, including temporal convolutional network (TCN)-based detector and deep neural network (DNN)-based estimator. Specifically, the TCN-based detector incorporates the locally time-series observations and their time derivatives as inputs to achieve precise fault detection rapidly. Based on the fault detection results, a reference tracking scheme is developed, where the estimations of the DNN-based estimator serve as references for a PI controller to compensate the system. To improve the interpretability of the estimator, a physical constraint derived from droop control is added to the offline training process, which ensures accurate recovery of the AC bus frequency, point of common coupling (PCC) voltage, and active/reactive power sharing. Finally, the effectiveness of the proposed method is confirmed through real-time experiments in OPAL-RT.
A substantial body of academic work has investigated reinforcement learning for Volt/VAR control (the process to manage voltage levels and reactive power to maintain voltage limits and reduce losses), but documented industrial adoption remains largely absent. The gap in practically deploying such theoretically advanced methods stems from utilities’ caution about online RL, where risky exploratory actions could trigger voltage violations or equipment stress. Meanwhile, offline RL has not been widely investigated in the power system domain because routine operational logs are often viewed as insufficiently informative for long-horizon policy improvement, rather than being collected with deliberate exploration for RL. In this work, we show that routinely collected SCADA, AMI, and controller logs encode time-stamped state–action–outcome trajectories that can be reorganized into Markov decision process (MDP) transitions for purely offline learning. However, because the data are passively collected rather than generated through active experimentation, the data inevitably include noise, limited observability, and heterogeneous control behaviors, which distort value estimation and degrade policy learning. To improve robustness against limited state–action support and heterogeneous log quality, we adopt Conservative Q-Learning (CQL) as a representative conservative offline RL approach to mitigate action extrapolation and overestimation during policy improvement from fixed logs. Case studies on IEEE 13-, 123-, and 8500-node feeders demonstrate that offline RL policies trained solely from logs approach the performance of online RL policies trained with extensive exploration, with increasing data from emulated operating scenarios. By reusing historical operation data, offline RL can achieve stronger performance in the initial learning stage compared to online RL during early exploration in our case studies, reducing reliance on exploratory online interactions for policy improvement.
A fundamental question is investigated in this paper: Why does the Fast Decoupled Load Flow (FDLF) converge poorly for distribution networks with large R/X ratios? The intuitive reason is that resistances are ignored in the B′ matrix used in the P-θ correction equations. However, Monticelli et al. have pointed out the opposite: Ignoring resistances in the B′ matrix is, in fact, more accurate than adding them back, and the correction equations used in the FDLF are equivalent to those in the constant Jacobian for radial networks. To answer this question, this paper revisits the approximations introduced in the derivation of the fast decoupled scheme from the Newton-Raphson method. This paper then demonstrates that the primary reason for the deterioration in convergence with increasing R/X ratios is the growing values in intermediate voltage updates. Utilizing the newest values of state variables tends to counter such effects to a certain degree, thus improving convergence in most cases. Case studies conducted on the 33-bus, 69-bus, 118-bus (with multiple load power levels), and 423-bus radial distribution systems confirm the theoretical explanations. These results improve the theoretical understanding of FDLF convergence and provide a basis for diagnosing and evaluating decoupled power-flow formulations in networks with strong active–reactive power coupling.
Although soft open points (SOPs) enhance regulation in distribution networks, existing planning studies often fail to account for device lifetime, leading to inaccurate cost evaluation and suboptimal siting and sizing decisions. To address this issue, this paper proposes a life cycle cost (LCC) oriented SOP planning strategy that accounts for device failure mechanisms. First, a quantitative evaluation method for device lifetime under operation mission profiles is established. Second, a bi-level planning model is formulated to incorporate device lifetime and replacement cost. Third, a two-stage renewable-power scenario construction method is adopted to represent the long-term mission profile with a limited set of representative scenarios for lower-level operational optimization and lifetime evaluation. Finally, a hybrid grey wolf optimizer (GWO) and second-order cone programming (SOCP) solution strategy is used to solve the planning model while maintaining computational tractability. Case studies on the IEEE 33-bus and IEEE 15-bus systems demonstrate the effectiveness of the proposed planning strategy. Sensitivity analyses further show that increasing PV integration raises both the LCC and replacement cost, while the lifecycle economic performance is more sensitive to the discount rate and electricity price than to the maintenance-cost coefficient. A scalability test on a 102-node composite distribution system further verifies the applicability of the proposed strategy, achieving a 33.36% reduction in total LCC compared with conventional planning.
With the increasing complexity of extreme event evolution process and the widespread integration of inverter-based DGs, distribution system (DS) restoration faces multiple risks such as subsequent faults and renewable energy output uncertainties. Neglecting these risks in restoration may lead to unexpected load shedding or even larger blackout. Existing works have not sufficiently considered these risks in DSs, especially cascading effect of subsequent faults. This paper proposed a DS restoration model considering the above two types of risks. Firstly, for subsequent faults, a node-microgrid affiliation identification model is designed to characterize the cascading process of “fault occurrence-protective device triggering-sudden frequency fluctuation” within each microgrid with flexible boundaries yet to be optimized. This facilitates the identification of DG status after subsequent faults and the integration of risk mitigation in restoration optimization. Secondly, for renewable energy uncertainties, robust constraints are formulated to ensure DG maintains necessary regulation capacity against renewable energy output deviations, preventing secondary interruption of the load already been restored. Finally, the model is formulated as a mixed-integer linear programming problem. Numerical results validated that the model can effectively avoid severe consequences while ensuring satisfactory restoration performance.
As electricity prices become increasingly volatile due to the growing penetration of renewable energy sources, Energy Storage Systems (ESS) are encountering greater opportunities for inter-temporal arbitrage. These can be harnessed through participation in electricity markets using a predict-then-optimize framework: a forecasting model first predicts prices, which are subsequently used in a profit maximization problem. Decision-Focused Learning (DFL) techniques, allowing to train forecasters to directly maximize profits of optimized decisions rather than minimizing statistical price forecasting errors, have been shown to increase profits. However, these techniques are computationally inefficient because they require solving the optimization problem across the entire training set for each training epoch. To address this issue, we introduce a machine learning proxy method mimicking the output of the optimization problem during training. Our approach leverages duality theory to retrieve decisions in two steps: (i) predicting a key dual variable with a pre-trained neural network, and (ii) applying smoothing functions to this prediction to determine the ESS (dis)charge decisions. In a case study involving an ESS participating in the day-ahead market with real-life data, we demonstrate that our proxy method significantly reduces training time compared to benchmark DFL methods, while achieving comparable or superior out-of-sample profits.
In parallel to the cyber attack that manipulates the reference points of distributed energy resources (DERs) by maliciously accessing the remote monitoring and control system, the vulnerability of voltage/current sensors to electromagnetic interference (EMI) in the physical domain has been widely discussed. Existing research efforts against sensor spoofing attacks can be classified into physical prevention and cyber detection/mitigation. These defence methods each have strengths and weaknesses in balancing cost, security, and performance in a single DER, yet systematic research on their multi-layer efficient coordination across DERs remains limited. Towards this end, this paper proposes a hierarchical framework to detect and mitigate sensor spoofing attacks in networked microgrids (NMGs) via multi-layer cyber-physical coordination. It requires only to deploy physical prevention technologies at critical points, i.e., the local points of common coupling (PCC) of MGs, such that cyber detection/mitigation algorithms can be adopted based on the secured sensor readings to counter sensor spoofing attacks in DERs. The framework employs an MG-DER coordinated proactive detection scheme to strategically trigger parameter perturbations, under which the intelligent sensor spoofing attacks can be effectively disclosed. Afterwards, mitigation schemes based on MG-DER coordination are activated to recursively and accurately estimate sensor biases. Experiments on a cyber-physical DC NMG testbed confirm the framework's effectiveness across diverse attack scenarios.
Precise and reasonable island partitioning of microgrids with distributed power sources is crucial for ensuring a continuous power supply to critical loads and enhancing the economic efficiency of fault recovery. This paper proposes a microgrid island partitioning strategy that integrates Cumulative Prospect Theory (CPT) and Transfer Learning. First, models of outage-related economic loss, network loss cost, and switching operation cost are built for island partitioning based on CPT. Second, to reduce the influence of probability on the prospect theory model, a decision weight function is introduced to reconstruct it, and an island partitioning objective function based on cumulative prospect value (CPV) is constructed. Then, the problem of island partitioning is described as a Markov decision process. Furthermore, to quantify users’ subjective perceptions of island partition, a comprehensive satisfaction assessment model is developed by incorporating load restoration quantity, restoration speed, and load restoration balance. To address the challenges of outdated experience and insufficient action optimization efficiency of the proximal policy optimization method under dynamic scenarios, a double experience pool mechanism with oblivious priority is designed. Finally, based on the Proximal Policy Optimization method with the Double Experience and the Oblivious Prioritized Experience Replay Mechanism (DOPER-PPO), the decision-making process is trained to obtain the optimal strategy. The effectiveness of the proposed strategy is evaluated based on the improved IEEE-69 node system. Results show that the proposed strategy can effectively improve the reliability and economic performance of microgrid power supply.
As energy-intensive industries, modern Coal Mine Integrated Energy Systems (CMIES) are transitioning to decarbonized and sustainable energy systems. Due to the complex operational models and reliance on human expertise, traditional CMIES operation fails to efficiently balance conflicting objectives of cost minimization, carbon emission reduction, and maximal Associated Energy Source (AES) utilization. To overcome these limitations, this paper presents a multi-objective optimization model for CMIES operation that leverages AES utilization and the coordination between coal transportation and mine drainage systems. Diverse equipment for AES utilization are modelled to recover energy from coal mining byproducts. Meanwhile, the Multi-Objective Optimization with Reinforcement learning and Embedded-knowledge (MOORE) algorithm is proposed, dynamically extracting and embedding evolutionary process knowledge through deep Q-learning networks to the evolutionary guidance strategies without human intervention. The approach integrates three guidance strategies with adaptive selection based on real-time population states. Simulation results on a real CMIES demonstrate MOORE achieves superior performance on the Pareto front of the cost saving, carbon emission reduction, and AES utilization enhancement. Also, the diversity and distribution uniformity of the solutions, measured by hypervolume and inverted generational distance, are considerably improved when compared to other benchmarks. Results indicate the proposed method significantly advances multi-objective evolutionary algorithms for industrial applications.
With the increasing integration of renewable energy sources, price-responsive flexible loads (PRFLs) have become a critical resource for maintaining grid supply-demand balance. Exact aggregate models (AGMs) are essential for system operators to predict load responses and leverage their regulatory capabilities. Although physics-informed data-driven methods are widely adopted for their interpretability, existing research has predominantly concentrated on enhancing predictive accuracy, often overlooking the practical identifiability (PI) of model parameters. A model lacking PI, even if it accurately fits historical data, remains an unreliable “black box” and consequently poses risks to system operations. To address this issue, this paper proposes a comprehensive modeling framework for PRFLs based on PI analysis, highlighting the selection of the AGM structure. The framework introduces a two-stage PI assessment process: 1) a fast screening stage employing the radial penalty approach to efficiently identify potentially unidentifiable parameters with minimal computational cost; 2) a refined analysis utilizing the extended profile likelihood for in-depth diagnostics, investigating the root causes of PI issues, such as strong parameter correlations and insufficient data information. Numerical tests across various PRFL scenarios demonstrate that high predictive accuracy can be misleading. Specifically, the models lacking PI, despite performing well on training and test datasets, may infer physically feasible regions that significantly deviate from reality and fail completely during validation. The results confirm that the proposed framework can effectively identify these deficiencies that the accuracy metrics alone cannot detect.
Due to the harsh operating environment and the reliance on communication networks, distributed microgrids (MGs), as a typical form of cyber-physical systems (CPSs), are highly vulnerable to actuator faults in the physical layer and cyber attacks on communication links, leading to system instability. Existing studies rarely address these two issues simultaneously, mainly because the cyber and physical layers are dynamically coupled yet asynchronous in their information sources. This paper investigates the distributed cooperative secondary control problem for hybrid AC/DC MGs under hybrid cyber attacks and actuator faults. Specifically, a physics-informed neural network (PINN) incorporating droop equations and a representation subspace distance (RSD) term is developed to predict the secondary control signals directly from local measurements. In addition, a conditional switching compensation mechanism is proposed to correct the abnormal secondary control signals caused by hybrid disturbances. Compared with existing data-driven control approaches, the proposed RSD-PINN control method exhibits superior generalization capability across various load conditions, thereby improving its adaptability to changing operating environments. Finally, the safety and effectiveness of the proposed method are verified through Lyapunov-based theoretical analysis and real-time hardware-in-the-loop experiments.
With the rapid proliferation of heterogeneous flexible resources (HFRs), such as microgrids and virtual power plants, hierarchical dispatch has become essential, making aggregate modeling a crucial foundation for resource coordination. Existing methods typically decouple the aggregate feasible region (AFR) of HFRs from the aggregate cost function (ACF). This separation isolates physical constraints from economic signals, preventing operators from quantifying the marginal value of flexibility and causing modeling redundancy. To solve this, we propose a feasibility-embedded aggregate cost function, unifying feasibility and cost into a strictly convex scalar interface. First, by implicitly representing physical limits as steep economic penalties, we recast the decoupled aggregation of AFR and ACF into a unified fitting problem. Second, a tailored multi-scale input-convex neural network is developed to resolve the inherent conflict between approximating smooth operational costs and capturing sharp feasibility barriers. Numerical results validate that the proposed interface achieves superior accuracy while maintaining a highly compact formulation.
Learning-based anomaly detection is increasingly adopted in grid-tied photovoltaic (PV) systems. Advanced multi-variate detectors implicitly learn both temporal dynamics and inter-channel spatial correlations from tightly coupled sensor telemetry, forming a powerful defense against data manipulation. Conventional adversarial attacks (AAs), which treat the feature space as unconstrained, generate physically inconsistent “ghost data” that violate these correlations and are therefore readily detected. This paper systematically investigates whether such spatiotemporal-aware detectors remain vulnerable to carefully designed perturbations. We show what they do: the proposed stealthy adversarial attacks (SAAs), based on physics-constrained projected gradient descent, optimize perturbations within a root-feature subspace and reconstruct all dependent channels through a differentiable physical layer, such that every adversarial sample is confined to the physical manifold and preserves temporal and spatial consistency by construction. A manifold-geometric analysis explains why such on-manifold perturbations are indistin-guishable to any detector that flags anomalies by their departure from the learned benign manifold, and a controlled ablation isolates the spatial-algebraic and temporal-coherence mechanisms behind the evasion. Hardware-in-the-loop experiments against four detectors — including the spatiotemporal graph-based DST-GNN — show that SAAs achieve attack success rates exceeding 86%, drastically outperforming AAs. We further demonstrate that the attack remains effective under LCL-parameter mismatch and time-varying irradiance/temperature, generates each masked window within a single rolling window including 50 sample points on commodity hardware without a dedicated accelerator — although sustaining this at the full per-sample rate remains beyond a single device — and induces sustained, quantified over-voltage that the blinded detectors fail to alarm, revealing a critical vulnerability of residual/forecasting-based spatiotemporal anomaly detectors in grid-tied PV systems.
To enhance the adaptability and performance of existing pilot protection in multi-terminal smart DC distribution systems, this paper proposes a novel pilot protection scheme based on the transient current integral increment. First, the current characteristics at both ends of the DC line during internal and external faults are theoretically analyzed, providing the foundation for the protection principle. Then, an integral increment function is introduced to reliably extract fault features using short data windows, balancing computational efficiency and reliability. Based on this, a pilot protection scheme is developed to achieve accurate fault identification and ensure coordination between protective devices. The scheme demonstrates robust performance under various fault conditions. Finally, extensive tests conducted in PSCAD/EMTDC and on a Hardware-in-the-Loop platform validate the effectiveness of the proposed method. Results demonstrate that the proposed pilot protection scheme achieves rapid and reliable DC fault detection, offers strong adaptability to variations in topology, transition resistance, and fault location, and exhibits high immunity to a wide range of disturbances, including noise, lightning interference, DG/load fluctuations, communication delays, and startup timing errors.
With rapid deployment in commercial and public buildings, building ice storage systems (BISS) have emerged as a new type of flexible resource. By fulfilling cooling demands through the phase transitions and heat transfer among ice, water, and air, BISS can provide multi-time scale flexibility to power systems. However, accurately quantifying this flexibility remains challenging. Existing models struggle to balance accuracy, physical interpretability, and computational tractability. Additionally, a unified mechanism to evaluate flexibility across varying time scales is lacking. To this end, we propose a physics-constrained neural ordinary differential equations framework for BISS modeling. Specifically, a mode-conditioned constraint network is designed to inherently satisfy mode-dependent thermodynamic constraints through a projection-based differentiable layer. Furthermore, sub-network decomposition and convolutional historical encoding are combined to capture the heterogeneous dynamics of ice, water, and air. Based on this tractable model, a two-stage optimization algorithm incorporating piecewise linearization and gradient descent is developed to evaluate flexibility across multi-time scales. Case studies on a Modelica-based simulation platform demonstrate that the proposed approach achieves higher modeling accuracy than existing methods while ensuring reliable flexibility quantification.
This paper proposes a model-based deep reinforcement learning (DRL) framework for microgrid energy management built on a Dreamer-style world model. The approach jointly learns a latent dynamics model of the microgrid and a continuous control policy, and uses multi-step imagination roll-outs for prediction-based decision making under AC power-flow and operational constraints. Since actions are evaluated inside the learned model before being applied, operators can inspect predicted trajectories to see how decisions affect future costs and network states. The method is tested on three distribution-level microgrids. Across all cases, the proposed method achieves substantially higher sample efficiency than widely adopted model-free RL benchmarks, reaching near-asymptotic performance within a few thousand environment steps while these benchmarks require tens of thousands or fail to converge. The learned policies further achieve a favorable balance between operating cost and safety violations relative to state-of-the-art model-free and model-based RL baselines, approaching the performance of an idealized mixed integer programming-based benchmark with perfect foresight.
