Traditional model-based participation factor calculations in power systems often suffer from parameter inaccuracies. While data-driven Koopman methods offer an alternative, they face the curse of dimensionality due to the difficult selection of observables, drastically restricting their scalability, especially when incorporating algebraic variables. To address these challenges, we propose a unified, deep-learning-enhanced Koopman operator framework. First, we introduce an augmented Koopman operator capable of computing participation factors for both state and algebraic variables. Second, we integrate this operator into an autoencoder to automatically learn optimal observable functions, ensuring scalability for large-scale systems. Illustrative examples on the IEEE 9-Bus and the IEEE 118-Bus modified test systems are carried out to demonstrate the method’s effectiveness and verify its ability to guide stability enhancement.

The computational speed of electromagnetic transient programs (EMTP) is severely limited by both the curse of dimensionality and the ill-conditioned system matrix, which collectively degrade solver performance. However, existing research on EMTP acceleration has largely overlooked the issue of ill-conditioning. This letter presents a first systematic, EMT-oriented investigation of the ill-conditioning of the EMTP admittance matrix by establishing a link between its physical origins and mathematical pathologies, thereby revealing the underlying mechanism by which network topology induces ill-conditioning. Building upon these structural insights, a preconditioner-based strategy is developed that significantly accelerates computation while preserving numerical accuracy. Simulation results demonstrate the outstanding efficiency and robustness of the proposed approach.

Abstract This study presents a scenario-based stochastic optimization framework for the co-planning of distributed PV and battery storage systems in distribution grids. To account for uncertainties in solar generation and load consumption, a scenario matrix is generated via the Heuristic Moment Matching (HMM) approach. This matrix is subsequently combined with deterministic power flow formulations, yielding a stochastic optimization model that determines the optimal placement and capacity of storage units, with the goal of maximizing the system’s net present value (NPV). Simulations on the IEEE-53-bus test system reveal that the proposed approach substantially enhances economic performance through effective peak–valley arbitrage enabled by energy storage. Compared to deterministic planning approaches, the stochastic model also enhances system reliability by substantially reducing bus voltage violations and unmet load rates under uncertain conditions.

Under the carbon neutrality target, the energy transition of power systems requires a well-designed long-term generation expansion plan to ensure safe, stable, and low-carbon operation. To address the challenge of centralized planning failing to balance generation expansion and load development effectively, a market-driven multi-stage generation expansion planning (MMGEP) model is proposed, which incorporates the supply function equilibrium model to simulate bidding behavior in the electricity market, leveraging market forces to guide generation planning and incentivize demand response. The MMGEP model is formulated as a game-theoretic optimization problem and further reformulated into a single-layer quadratic programming model to reduce the computational complexity. Moreover, the latest capacity tariff mechanism is integrated into the MMGEP model to evaluate its effectiveness in guiding planning and reducing energy supply costs. Additionally, the optimal capacity tariff pricing range for enhancing the cost competitiveness of thermal power units is identified. A case study based on the latest real-world data from Jiangsu Province in China demonstrates the advantages of the MMGEP model over the centralized planning model and emphasizes the effectiveness of introducing market mechanisms into generation expansion planning.

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.

Accurately identifying the connectivity between transformers and downstream three-phase customers in low-voltage distribution networks is challenging, because voltage curves of different phases and nearby nodes can be weakly distinguishable, especially when adjacent transformers on the same feeder serve geographically close customers with highly similar voltage curves. This paper proposes a novel method based on load-switching fluctuation characteristics recorded by smart meters. By extracting localized current and voltage fluctuations and establishing correlation matching, the method overcomes the limited discriminability using steady-state measurements. The method operates in two stages: first, switching-induced fluctuation characteristics are extracted and matched to cluster customers by the supplying transformer and phase; second, cross-phase fluctuation characteristics are exploited to merge the above clusters into complete transformer-customer groups. Case studies demonstrate that the proposed method improves the accuracy of connectivity identification compared to traditional correlation-based methods, particularly in scenarios with highly similar voltage curves, and remains reliable under typical practical conditions.

The global decarbonization is driving integrated energy systems (IES) toward more efficient and low-carbon operations, with tighter coupling between natural gas systems (NGS) and electric power systems (EPS) to accommodate diverse renewable sources and energy carriers. The bidirectional energy flow problem in IES with a partial differential algebraic equations (PDAE) form remains a challenge for model-based solvers due to privacy concerns and computational complexity, as it may require full parameters and dozens of minutes or hours to obtain a feasible solution in large-scale systems. To address this obstacle, this study proposes a physics-informed neural operator for energy flow calculations in IES. A novel Differential-Algebraic Gas Flow Neural Operator (DAGFNO) is proposed to embed physical constraints of PDAE into the neural operator, which not only obtains accurate heterogeneous gas states but also provides a privacy-preserved interface for EPS analysis. Besides DAGFNO, we also developed a novel Masked Differential and Algebraic Coupling Constraint Loss function (MDACloss) to represent the degree of constraint violation and enable its parallel computing ability through the masking technique. By doing so, the MDACloss could guarantee the satisfaction of constraints in the energy flow calculation of IES obtained by the DAGFNO as much as possible. Case studies on two NGS and EPS coupled IESs reveal the effectiveness of the proposed method.

The integration of renewable energy alongside other energy sources into modern power systems has markedly transformed them, posing new challenges in their operation and control. Currently, the ubiquitous deployment of metering devices has laid the groundwork for the proliferation of data-driven methodologies. In this context, the Koopman operator is increasingly gaining attention as an interpretable, data-driven, and model-free approach. This paper explores the principles and applications of the Koopman operator, aiming to bridge theoretical concepts with real-world challenges in nonlinear power systems. Initially, the paper lays out the theoretical foundations of Koopman theory and discusses mainstream approximation algorithms for the Koopman operator, offering a systematic framework for preserving nonlinearities linearly. Second, we elaborate on various Koopman-based applications, including system identification, state estimation, data-driven control, stability evaluation, and uncertainty quantification, and conclude with a summary of their potential applications across different energy systems. Finally, four key challenges for the future development of Koopmanism are presented and discussed.

Accurate and concise modeling of district heating networks (DHNs) is essential for reliable operation and control, but it remains challenging in practical engineering where measurements at some source or load nodes are completely unavailable. To address this knowledge-intensive modeling problem, we propose a virtual-node-based aggregate model (VN-AGM) and a physically informed data-driven identification method for DHNs under missing node measurements. The central contribution is an explicit and interpretable representation of incompletely observed DHNs, in which unmeasured load or source nodes are equivalently aggregated into a single virtual node while preserving the thermal mapping and hydraulic consistency of the original network. First, we derive the VN-AGM for the DHN with unmeasured load or source nodes, revealing that the load (or source) nodes without measurements can be equivalently aggregated into a virtual node. Second, we formulate the parameter identification model of the VN-AGM, the structural identifiability of which is then analyzed to clarify how physical knowledge supports reliable model construction under limited sensing conditions. Third, the mass flow rate distribution relationship between source and load nodes is embedded as a reasoning constraint, enabling parameter identification without requiring additional measurements beyond the available field data. Finally, we develop a two-stage lasso regression-based parameter estimator for the VN-AGM, which embeds the structural constraints of DHN to improve the robustness under practical measurement errors. Case studies on 51-node and 226-node DHNs demonstrate that the proposed method provides a scalable and practically deployable tool for supporting DHN modeling, operation, and control under incomplete observability.

Hydrogen serves as a pivotal intermediary in linking renewable energy integration with diverse energy demands. This coupling introduces multiple uncertainties into the system, posing challenges for effective scheduling. This paper proposes a novel mixed-integer multi-stage distributionally robust optimization (MIMS-DRO) framework for the adaptive scheduling of hydrogen-based integrated energy systems (H-IESs) under multiple uncertainties. To accurately depict high-dimensional uncertainties stemming from uncertainty-type multiplicity and scheduling-stage proliferation, we develop an innovative structured mixture ambiguity set, which fully exploits the statistical independence structure between low-dimensional uncertainty components while encoding the feature of multi-modality, thus substantially mitigating conservatism. Based on this ambiguity set, we formulate the MIMS-DRO scheduling problem, where variables related to hydrogen-to-ammonia are treated as here-and-now decisions for stable production while the remaining dispatch variables serve as mixed-integer recourse decisions. Subsequently, we establish theoretical set-inclusion relationships for related ambiguity sets and prove the finite-sample guarantee for the proposed framework. To efficiently solve the resulting scheduling problem, we develop a tailored solution methodology that leverages a lifted decision rule to achieve adaptive and non-anticipative scheduling, and derive an equivalent mixed-integer linear programming reformulation as opposed to the relaxed reformulation in the existing literature. Case studies demonstrate that the proposed scheduling approach is more cost-effective than the state-of-the-art methods.

An impedance model is being adopted for the stability analysis of power electronic systems. Due to limited accessibility to detailed controller information, the analytical impedance model is difficult to derive. This letter proposes an impedance identification method based on the Kolmogorov-Arnold network (KAN) and physical information for grid-connected converter systems with grid-following and grid-forming control. Leveraging the Kolmogorov-Arnold representation theorem, the proposed two-layer KAN replaces fixed neuronal weights with learnable univariate spline functions, thereby achieving universal approximation with fewer trainable parameters and reduced network depth than a multilayer perceptron with comparable accuracy. The effectiveness of the proposed method is validated by wind farms with doubly fed induction generator converters in the real-time digital simulator and compared with other neural structures.

The rapid proliferation of distributed photovoltaic (PV) systems presents significant challenges for accurate power generation forecasting due to their inherent intermittency and spatial-temporal variability. This paper proposes a novel framework that leverages pre-trained large models for distributed PV power forecasting by integrating retrieval-augmented generation with cross-modal semantic alignment. To unlock the reasoning capabilities of pre-trained large models, we design a scenario-consistent RAG module that retrieves relevant historical PV sequences guided by long-term dependencies and temporal correlations, and integrates them through a Chain-of-Thought prompting paradigm. Furthermore, we develop a cross-modal semantic alignment mechanism to bridge the representational gap between numerical PV series data and the language semantic space of PLMs, enabling effective pattern recognition across modalities. To ensure physically meaningful forecasting within the training and inference processes, we also establish a constrained activation function that explicitly considers the inherent characteristics of PV power generation. Extensive experiments on nine real-world distributed PV datasets demonstrate that our framework achieves state-of-the-art performance, significantly outperforming six benchmark models.

Accurate probabilistic modeling of renewable power is essential for the secure operation and control of modern power systems. However, learning and modeling the data structure with high accuracy remains challenging due to the inherent spatial-temporal correlations of renewables. To address this issue, we propose a novel quantum-assisted Gaussian-Bernoulli restricted Boltzmann machine (GBRBM), which is intrinsically suitable for continuous wind power modeling. Furthermore, we tailor its negative phase to be directly solvable by quantum computing, thereby accelerating the learning process. Experiments conducted on real quantum hardware validate the cost-effective performance of the proposed method.

Although carbon flow is a powerful tool for assigning emission responsibility to consumers, it has not been explored in hybrid AC-DC systems. This paper presents a novel probabilistic carbon-flow model to quantify the distribution of carbon intensity in such systems. To further characterize the importance of uncertain inputs, such as renewable energy and loads, on probabilistic carbon flow, a global sensitivity analysis (GSA) strategy is introduced. To alleviate the computational burden of traditional Monte Carlo methods in quantifying these metrics, it incorporates an adaptive polynomial chaos expansion (PCE)-based surrogate model. This significantly reduces the computing burden while maintaining high statistical accuracy. Simulations validate the proposed carbon flow model in the hybrid AC-DC system and reveal the excellent performance of the PCE-based GSA method.

The low-carbon energy transition faces the challenges of uncertainty from high renewable energy penetration and the economic reconstruction of traditional fossil fuel regions. Repurposing abandoned oil wells (AOWs) provides an alternative option to facilitate the low-carbon transition and revitalization of these oilfields. This paper aims to propose a novel hydrogen hub-centered oilfield integrated energy system (HH-OIES) to resolve the aforementioned challenges. Synergistic hydrogen-heat repurposing of AOWs can be achieved through integrated hydrogen production, storage, and multi-pathway utilization across various oilfield zones. Furthermore, a multi-objective transition planning and optimization framework for the HH-OIES is developed to overcome the limitations of relying solely on AOWs for heat supply, which cannot adequately address the intermittency of renewables. To solve the proposed model, we introduce a Global Envelope Interval Optimization method.Its solution space enveloping technique effectively handles the planning and operation of complex, large-scale systems, enabling a synergy between economic and low-carbon objectives under varying risk preferences while significantly reducing computational complexity. Simulation results demonstrate the role of the HH-OIES in advancing oilfield transition and validate the effectiveness of the proposed solution method.

The unit commitment (UC) of the heat and electricity integrated energy systems (HE-IESs) is a fundamental issue in ensuring safe and economical operations, which requires predictions of renewable energy and load. In the traditional predict-then-optimize UC (TPO-UC) framework, the training process of the predictor is performed before and independently of the UC optimizer, potentially leading to suboptimal outcomes as it fails to account for the downstream UC optimizer’s concern about the prediction error. Considering this, this article proposes an improved UC framework for the HE-IES by integrating the concern of the UC optimizer into the predictor. First, we introduce the smart predict-then-optimize UC (SPO-UC) framework for the HE-IES, formulated as a bilevel mixed-integer linear programming (BiMILP) model. Second, we design a primal heuristic for SPO-UC to address the computational challenges, namely modified approximate reformulation and decomposition (MA-R&D), which is proved to converge to a stationary point of the equivalent single-level reformulation of BiMILP within finite iterations. Particularly, the proposed MA-R&D algorithm does not rely on the relatively complete response assumption and also accounts for the connection constraints in the SPO-UC model, which have not received attention in existing studies. Finally, case studies verify that the proposed SPO-UC outperforms the popular TPO-UC and the state-of-the-art SPO-UC methods in the HE-IES, and the proposed algorithm greatly improves computational efficiency.

With the increasing penetration of renewable resources in modern power systems, scenario generation for renewable energy has emerged as a critical tool for system operation and planning. Among the widely studied methods, Generative Adversarial Networks (GANs) are popular. Despite its model-free nature, it suffers from high computational demands due to its extensive trainable parameters and often struggles to capture intricate data patterns. To address these challenges, we employ quantum computing techniques that harness quantum entanglement principles. We propose, for the first time, a method of generating a quantum-enhanced renewable energy scenario based on a hybrid quantum GANs (QGANs) architecture. Specifically, given historical data of renewable resources, we design a quantum generator using parameterized quantum circuits. This quantum neural network achieves superior expressivity compared to its classical counterparts while requiring significantly fewer trainable parameters. Then, the resulting QGANs architecture combines this quantum generator with a classical discriminator for the effective generation of renewable energy scenarios. Quantum measurements also inherently introduce randomness into the generated renewable scenarios. The simulation results verify the rationale of the proposed method and demonstrate its effectiveness in capturing the spatio-temporal characteristics of renewable resources.

Driven by the objectives of carbon neutrality, renewable energy sources including wind power have experienced rapid development. Electromagnetic transient simulation has emerged as a critical tool for analyzing and validating the performance of wind energy conversion systems (WECSs). This article proposes an equivalent circuit modeling of WECS based on hybrid numerical integration methods for real-time simulation, which preserves a constant admittance matrix of the back-to-back voltage source converter (B2B VSC) across different switching states and eliminates the need for additional switching circuits under pulse-blocked conditions. Furthermore, the proposed model achieves decoupling between the rectifier and inverter stages of the B2B VSC without introducing artificial delay, thereby enhancing simulation accuracy. The effectiveness and efficiency of the proposed modeling approach are validated through the implementation of the WECS on a real-time simulation platform and hardware-in-the-loop test.

An aggregate model that accurately quantifies buildings' thermal flexibility is an essential interface for energy system operation. However, privacy concerns and measurement inaccuracies make obtaining an accurate aggregate model challenging. To address this, we propose a privacy-preserved robust parameter estimation approach to get the aggregate model of buildings. The proposed method ensures the accurate modeling of the aggregate thermal dynamics of buildings against outliers in measurements, without exposing any sensitive information from end users. The effectiveness of the proposed method is validated through numerical tests.