When leveraged within carbon market mechanisms, hydrogen energy storage systems (HESS) offer a viable option for supporting low-carbon operation in vertically integrated utilities. However, a key challenge is that short-term operational decisions are made without explicit visibility of their long-term consequences, which are reflected through cumulative hydro gen and carbon constraints that ensure system feasibility. To bridge this time-scale gap, this paper proposes a reinforcement learning–augmented primal–dual rolling-horizon optimization framework. A trained future-aware regularizer incorporates long-term information into short-term decision-making, while a primal–dual scheme enforces cumulative constraints on hydrogen and carbon markets with computational tractability. Numerical studies on the IEEE 6-bus, 118-bus, and 300-bus test systems demonstrate the framework's effectiveness and scalability. Results demonstrate that the proposed framework keeps annual terminal residuals negligible while reducing peak emissions, improving economic performance, and enabling seasonal load shifting across different system scales.

In this paper, a multi-agent distributionally robust reinforcement learning approach is proposed to solve the crew dispatch problem for service restoration in the distribution network. The proposed approach leverages a novel representation of the environment formulated as a Markov decision process. The model of the environment incorporates the energy management problem as a linear programming problem, which yields the volume of the restored load to determine each agents reward. The optimal repair and restoration policy is determined using a distributionally robust multi-agent soft actor-critic (DR-MASAC) algorithm. The developed framework is applied to the service restoration in the modified IEEE 37-bus and the IEEE 123-bus test systems. The performance of the DR-MASAC algorithm is compared with the multi-agent soft actor-critic and multi-agent deep deterministic policy gradient algorithms to demonstrate its superiority in increasing the mean value and decreasing the standard deviation of the cumulative reward and average episode length during the training phase. The higher mean reward reflects a larger weighted restored load, while the lower standard deviation ensures consistent restoration policy performance under varying conditions. Shorter episodes indicate fewer restoration actions to restore the load. The performance of the proposed multi-agent algorithm is further evaluated during testing using the cost and the volume of unserved load as systemwide measures.

Power distribution system (PDS) restoration using distributed energy resources (DERs) demands sequential switching decisions that satisfy strict operational constraints. Existing multiagent reinforcement learning (MARL) approaches suffer from unstable policy updates, constraint violations, and poor generalization due to indirect value-based learning and posthoc feasibility corrections. We propose constraint-aware generative MARL (CGenMARL), a cooperative MARL framework built on three integrated components: a soft actor–critic backbone for stable, direct policy optimization to mitigate environment nonstationarity; a constraint-guided adversarial generator that embeds feasibility enforcement directly into learning via a centralized discriminator acting as a learned surrogate of the constraint manifold; and attention activation regularization to reduce overfitting through stochastic attention dropout, which prevents convergence to fixed coordination pathways and forces agents to rely on robust structural features. On the IEEE 123-bus and 8500-node systems, CGenMARL improves restored power by 8.79% and 8.66% over the best baseline, achieves zero constraint violations, and converges faster than state-of-the-art methods.

This paper aims to improve the resilience of the distribution network by forming microgrids in the aftermath of an outage using reinforcement learning (RL). The RL agent learns to determine the status of network switches to form the microgrids and manage the dispatch of distributed energy resources to serve the loads within microgrids. A hybrid randomized ensemble soft actor-critic (HRESAC) algorithm is developed to determine the optimal microgrid formation policy that includes the switching (discrete) and the generation resources dispatch (continuous) actions. The proposed algorithm is applied to the modified IEEE 37-bus and IEEE 123-bus test systems. The results show that the proposed method outperforms the benchmark algorithms in both training and testing. It achieves the highest cumulative reward during training, the highest prioritized average restored load, and the lowest unserved load during testing. Additionally, a dispatch interpreter algorithm is introduced to extract high-quality decision trees (DTs) from the optimal policy obtained by the HRESAC algorithm. It is shown that the procured DTs achieve 99.06% of the HRESAC policy's performance while using only one-twentieth of the parameters.

This paper introduces a decentralized, risk-averse operational framework for interconnected, unbalanced microgrids and the distribution system. Distribution system operation is modeled as a risk-averse optimization problem using conditional value-at-risk measures to enhance robustness against uncertainties in price-responsive demand bids. Microgrid operations are structured as scenario-based robust optimization problems, capturing the worst-case scenarios for demand and solar PV generation. Non-convex energy management problems within the distribution system and microgrids are reformulated as convex optimization problems using the moment relaxation technique. A decentralized scheme addresses heterogeneous uncertainties in microgrids and the distribution system. The framework is applied to two case studies: a distribution system connected to two microgrids and a modified IEEE 123-bus distribution system connected to four microgrids. The risk-averse optimization solution is compared to that of a stochastic programming approach. For the IEEE 123-bus system, the results show that introducing risk aversion decreases social welfare by 44.63% compared to the risk-neutral solution but improves the conditional value-at-risk by 44.04%. Additionally, the impacts of dispatchable resources, including energy storage and distributed generation, on operation cost, phase balancing, and uncertainty control at the main feeder are examined. It is shown that incorporating a statistical distance metric to regulate power flow at the main feeder decreases social welfare by 6.48%.

Networked microgrids (MGs) have emerged as a favored and promising scheme to facilitate the integration of distributed energy resources and enhance the resiliency of power support. To advance the flexible operation of distribution systems, this paper proposes an optimal scheduling model for networked MGs, embedding three innovative medium-voltage direct current (MVDC) technologies with voltage source converters, namely two-terminal back-to-back MVDC systems (BMSs), three-terminal BMSs, and multi-terminal BMSs. Compared to traditional MVDC systems, these newly introduced back-to-back MVDC technologies exhibit strengthened operational flexibility. We first formulate their explicit models based on real-world applications, incorporating constraints related to normal operation and power supply modes. Then, we present a day-ahead scheduling model for networked MGs equipped with these BMSs. Subsequently, we develop tractable reformulations for nonlinear constraints considered in the scheduling model, leading to a mixed-integer linear programming problem. Finally, numerical simulations on the IEEE 123-bus test system are conducted to demonstrate the effectiveness and superiority of the proposed scheduling model.

Accurate fault classification and location are critical to ensure the reliability and resilience of large-scale power distribution systems (PDSs). The existing data-driven works in this area struggle to capture essential space-time correlations of PDS measurements and often rely on deterministic and shallow neural architectures. Furthermore, they encounter challenges like over-smoothing and the inability to capture deep correlations. To overcome these limitations, a novel deep space-time generative graph convolutional autoencoder (SGGCA) is proposed. First, the PDS is modeled as a space-time graph where the nodes and edges show the bus measurements and line impedance values, respectively. The proposed SGGCA’s encoder captures deep correlations of the space-time graph using a new graph convolution with early connections and identity transformations to mitigate the over-smoothing. Our encoder encompasses a new recurrent method to adjust graph convolution parameters without relying on node embeddings on the temporal dimension. Additionally, it incorporates generative modeling by capturing the probability distribution function of the latent representation through a conditional normalizing flow model. The extracted generative space-time features are enhanced by a multi-head attention mechanism to better capture task-relevant characteristics of the PDS measurements. The extracted features are fed to sparse decoders to classify and locate the faults in the PDS. The feature sparsity of decoders ensures a high generalization capacity and avoids overfitting. The proposed method is evaluated on the IEEE 69-bus and 123-bus systems. It achieves substantial improvements in fault classification accuracy by 3.33% and 6.26% and enhances fault location accuracy by 6.33% and 5.73% for the respective PDSs compared to state-of-the-art models.

Ensuring the accurate detection of surface flaws in PV panels is vital for preserving energy efficiency and minimizing future repair expenses. Nevertheless, the diverse nature of these defects in terms of size, shape, and visibility presents significant localization challenges. Conventional models typically rely on fixed feature hierarchies, uniform spatial weighting, and static fusion strategies. These limitations restrict their ability to capture defects across scales, emphasize relevant regions, and integrate semantic information effectively under visually complex conditions. To overcome these challenges, we propose a Multi-Scale Attention-based Convolutional Neural Network (MSA-CNN), which is a compact detection framework composed of three specialized modules. The multi-scale feature extraction module first captures spatial patterns at varying resolutions through parallel convolutional branches, addressing scale-related limitations. These features are then refined by the dynamic attention module, which adaptively emphasizes defect-relevant regions based on spatial context. Finally, the context-aware fusion module integrates the attention-enhanced features by selectively combining multi-level information, producing semantically consistent representations for accurate detection. Experimental results on the PV Multi-Defect dataset show that MSA-CNN outperforms a range of state-of-the-art methods across all key detection metrics by achieving higher accuracy across all metrics and defect categories, with notable improvements in detecting small, low-contrast, and structurally irregular faults.

Fault location and classification are crucial to the reliable and resilient operation of power distribution networks (PDNs). Current machine learning works cannot provide accurate and reliable results for fault detection due to the lack of generalization power, feature sparsity, and capturing the interrelation information of adjacent PDN buses. Therefore, we propose a novel generative dynamic graph variational sparse coding framework for spatiotemporal fault detection. First, the PDN is modeled as a dynamic graph where the nodes represent the load and voltage sequence components of the buses, and edges show the impedances of the PDN lines. A dynamic graph variational autoencoder (DGVAE) is developed to learn the generative spatiotemporal features of the dynamic graph. The DGVAE incorporates a new edge propagation graph convolutional network with an attention mechanism into a deep recurrent model to capture the task-relevant spatial features of the PDN considering the interrelation information of nodes and the temporal features. Finally, a dictionary learning method is devised to learn the deep sparse representation of the captured generative features, which is mapped to the fault locations and classes. The proposed framework demonstrates superior results compared to the state-of-the-art benchmarks on the modified IEEE 69-bus and IEEE 123-bus PDNs in both fault location and classification tasks.

This work presents a distributed robust operation framework for the microgrids within the power distribution network. It addresses the uncertainties in photovoltaic generation, as well as active, and reactive loads in the network, by modeling them using polyhedral sets. The energy management problems are formulated as two-stage optimization problems in microgrids and power distribution networks for which Benders decomposition is used to solve the problems. The power flow constraints are relaxed using second-order cone relaxation and moment relaxation techniques in the power distribution network and microgrid energy management problems, respectively. The interaction between the microgrids and the power distribution network is represented using the price signal and the exchanged active and reactive power at the microgrids’ points of common coupling. The effectiveness of the proposed framework is shown using two case studies on IEEE 37-bus and IEEE 123-bus systems. The effect of the energy storage system on the operational cost of the system is assessed. It is shown that total operation cost is decreased by 9.69% when the energy storage system is integrated into the power distribution network. Additionally, the solution derived from the robust problem is compared with that of the deterministic problem.

Due to the increasing demand for electricity and the inherent uncertainty in power generation, finding efficient solutions to the stochastic alternating current optimal power flow (AC-OPF) problem has become crucial. However, the nonlinear and non-convex nature of AC-OPF, coupled with the growing stochasticity resulting from the integration of renewable energy sources, presents significant challenges in achieving fast and reliable solutions. To address these challenges, this study proposes a novel graph-based generative methodology that effectively captures the uncertainties in power system measurements, enabling the learning of probability distribution functions for generation dispatch and voltage setpoints. Our approach involves modeling the power system as a weighted graph and utilizing a deep spectral graph convolution network to extract powerful spatial patterns from the input graph measurements. A unique variational approach is introduced to identify the most relevant latent features that accurately describe the setpoints of the AC-OPF problem. Additionally, a capsule network with a new greedy dynamic routing algorithm is proposed to precisely decode the latent features and estimate the probabilistic AC-OPF problem. Further, a set of carefully designed physics-informed loss functions is incorporated in the training procedure of the model to ensure adherence to the fundamental physics rules governing power systems. Notably, the proposed physics-informed loss functions not only enhance the accuracy of AC-OPF estimation by effectively regularizing the deep learning model but also significantly reduce the time complexity. Extensive experimental evaluations conducted on various benchmarks demonstrate our proposed model's superiority over both probabilistic and deterministic approaches in terms of relevant criteria.

Energy storage systems (ESS) are indispensable building blocks of power systems with a high share of variable renewable energy. As energy-limited resources, ESS should be carefully modeled in uncertainty-aware multistage dispatch. On the modeling side, we develop a two-stage model for ESS that respects the nonanticipativity of multistage dispatch, and implement it into a distributionally robust model predictive control scheme. The ESS model features multiple selective operational modes, which enable its power interval to be scheduled in chronological dispatch. On the algorithm side, we propose to evaluate the future worst-case cost expectation over a convex relaxation of the non-convex and discrete value function of the recourse. This gives rise to a novel algorithm that efficiently solves a typical class of two-stage distributionally robust optimization problems, which are equipped with discrete recourse and infinite support. The advantage of the algorithm over the state-of-the-art nested column-and-constraint generation method is theoretically interpreted. Simulation is performed on the modified IEEE 118-bus system and 300-bus system. Results show that ESS function well on the basis of the proposed model and control scheme, and also demonstrate the superiority of the novel algorithm.

This paper introduces a novel deep learning-based framework for accurate fault localization and classification in power distribution systems. The proposed approach combines a long short-term memory (LSTM) network for capturing time-dependent features with a restricted Boltzmann machine (RBM)-based autoencoder for learning generative temporal characteristics of power system measurements. The deep sparse rectified linear unit (ReLU) neural network, guided by a Kullback-Leibler (KL) divergence-based sparse loss function, excels in fault location and classification. The computed sparse features reduce the overfitting chance as well as the required amount of data samples for training the deep neural network. Experimental results on the IEEE 123-bus system highlight the effectiveness of the proposed approach, showcasing reduced root mean squared error (RMSE) and mean absolute percentage error (MAPE) for fault location, along with higher classification and location accuracies compared to alternative methodologies. The superiority of the proposed approach is due to capturing unsupervised generative features as well as its high generalization power caused by feature sparsity.

Nowadays, rooftop photovoltaic (PV) panels are getting enormous attention as clean and sustainable sources of energy due to the increasing energy demand, depreciating physical assets, and global environmental challenges. In residential areas, the large-scale integration of these generation resources influences the customer load profile and introduces uncertainty to the distribution system's net load. Since such resources are typically located behind the meter (BtM), an accurate estimation of BtM load and PV power will be crucial for distribution network operation. This article proposes the spatiotemporal graph sparse coding (SC) capsule network that incorporates SC into deep generative graph modeling and capsule networks for accurate BtM load and PV generation estimation. A set of neighboring residential units are modeled as a dynamic graph in which the edges represent the correlation among their net demands. A generative encoder-decoder model, i.e., spectral graph convolution (SGC) attention peephole long short-term memory (PLSTM), is devised to extract the highly nonlinear spatiotemporal patterns from the formed dynamic graph. Later, to enrich the latent space sparsity, a dictionary is learned in the hidden layer of the proposed encoder-decoder, and the corresponding sparse codes are procured. Such sparse representation is used by a capsule network to estimate the BtM PV generation and the load of the entire residential units. Experimental results on two real-world energy disaggregation (ED) datasets, Pecan Street and Ausgrid, demonstrate more than 9.8% and 6.3% root mean square error (RMSE) improvements in BtM PV and load estimation over the state-of-the-art, respectively.

Distributionally robust optimization (DRO) has emerged as a favored methodology for addressing the uncertainties stemming from renewable energy sources. However, existing DRO frameworks primarily focus on single types of uncertainty characteristics, such as moments. Exploring novel ambiguity sets that encompass heterogeneous uncertainty information to mitigate decision conservatism is thus an essential and strategic move. This paper introduces a day-ahead optimal scheduling model tailored for electricity-hydrogen systems under renewable uncertainty, with embedded technologies of hydrogen production, storage, and utilization. Three novel ambiguity sets enriched with the moment, Wasserstein distance, and unimodality information are adeptly devised. Building upon these elaborated ambiguity sets, we develop efficient and scalable reformulations of the expected objective function and uncertain constraints, leading to either a tractable mixed-integer second-order cone programming problem or a linear programming problem. We validate the effectiveness and operating flexibility of the proposed electricity-hydrogen model using both a 6-bus test system and the IEEE 118-bus test system. Furthermore, we demonstrate the superior cost performance and computational efficiency of our developed DRO approaches.

This paper proposes a distributionally robust expansion planning framework for the gas-fired distributed generation in the interconnected distribution and natural gas networks with demand response. The proposed formulation accounts for the uncertainties associated with the electricity demand, natural gas demand, PV generation outputs, and demand bidding price. The ambiguity sets for the uncertain variables are constructed based on the Wasserstein distance. The expansion planning decisions are obtained under the worst probability distributions of the uncertain parameters. The problem is decomposed using Benders decomposition and solved in multi-stages to preserve the autonomous operation of the independent networks. The expansion planning of the gas-fired distributed generation is determined in the master problem, and the feasibility and optimality of the decisions in the power and natural gas networks are ensured using the corresponding sub-problems. The modified IEEE 34-bus distribution network connected with a 11-node natural gas network and the modified IEEE 123-bus system with a 28-node natural gas network are used to validate the efficiency of the proposed planning framework.

Effective fault location algorithms contribute to reducing the recovery and restoration time and improve the resilience of the power distribution networks. The existing machine learning-based approaches for fault location exhibit limitations, notably the absence of unsupervised feature learning, disregarding the capture of semantic features, and overlooking task-relevant features. This paper introduces the deep-attention Gated Recurrent Unit Gaussian Restricted Boltzmann Machine (GRU-GRBM) framework for fault location and classification. It combines an attention-enhanced GRU for accurate task-relevant temporal feature extraction, a GRBM-based autoencoder for unsupervised generative feature learning, and a sparse deep Rectified Linear Unit (ReLU) network with a mutual information (MI)-based dropout technique for supervised estimation of fault location and class. The proposed structure is shown to outperform the state-of-the-art methods on the IEEE 123-bus system through generative feature extraction, attention mechanisms, and feature sparseness.

This paper presents an equilibrium-based modeling framework for emergency response (ER) workload balancing for robust operations in metropolitan areas. The problem is formulated as a non-linear mathematical program (NLP), which determines the optimal maximum workload for each ER station such that the weighted sum of the area-wide expected response time and its variation is minimized. The concept of Marginal Cost of Uncertainty (MCU) is introduced to measure the impact of a station's workload increase on the robustness of the area-wide service performance. The solution of the NLP is proved to be equivalent to a state of equilibrium in which all stations have a minimum MCU. An iterative solution methodology is developed, which adopts a modified version of the Frank-Wolfe decomposition algorithm for convex optimization. The workload is iteratively balanced among adjacent stations until the state of equilibrium is achieved. At equilibrium, no station can reduce its MCU value by unilaterally shifting a part of its workload to any other station(s) in the area. The developed framework is applied to determine the optimal workload balancing strategy for 58 fire stations serving the City of Dallas. The framework is shown to enhance the robustness of the ER service performance especially in situations with imbalanced workloads.

Distribution service restoration plays a vital role in mitigating the adverse impacts of power outages stemming from extreme weather conditions. With incentives toward reducing the carbon footprint of power generation on the environment and the reliance on fossil fuel resources, the future distribution networks are equipped with distributed renewable energy sources. This paper reviews the state-of-the-art frameworks proposed for service restoration in the distribution networks with renewable generation technologies. First, the objectives of the distribution service restoration and the challenges to accomplishing this task are discussed. Later, the existing approaches to restoring the distribution networks and the control architectures are presented. The contribution of microgrid technology and the models used to incorporate renewable energy resources in distribution service restoration are discussed. In this context, the application of artificial intelligence to distribution service restoration is highlighted, and potential research opportunities in distribution service restoration are presented.

The increase in the generation capacity of the variable renewable resources and electricity demand introduces new operational challenges to the unbalanced three-phase distribution networks. This paper addresses the uncertainty associated with the ramping of net demand using a data-driven approach. A continuous-time optimization problem is reformulated to a linear programming problem using Bernstein polynomials. A distributionally robust optimization problem is formulated to capture the worst-case probability distribution of the net demand, which includes the demand and the PV generation. The solution to the distributionally robust operation of the unbalanced distribution network is compared to that of the stochastic programming problem in which the uncertainty associated with the net demand ramp is captured using scenarios. The developed formulated problem is validated using a modified IEEE 13-bus unbalanced distribution system. The impact of ramp limits of the main feeder on the expected operation cost of the distribution network is investigated.