The increasing penetration of virtual synchronous generators (VSGs) in power grids demands rigorous transient stability analysis, yet existing methods either yield overly conservative region of attraction (ROA) estimates or lack formal guarantees over continuous domains. This paper presents a boundary data-driven neural Lyapunov framework that concentrates training samples near stability boundaries, employs a parameterized architecture ensuring positive definiteness and radial unboundedness by construction, and integrates hierarchical verification with counterexample-driven refinement. The verification stage leverages satisfiability modulo theories (SMT) solvers to provide formal proofs over continuous state spaces. Experiments demonstrate that the proposed framework achieves tighter ROA estimates than classical energy function and quadratic Lyapunov methods while delivering formal stability certificates over continuous domains.

State-of-the-art soft-switching schemes, such as triangular current mode and quadrilateral current mode (QCM), create zero-voltage-switching conditions at the expense of increased current ripple. Although the turn-on losses of power devices are mostly eliminated, the conduction losses of power devices and the power losses in high-frequency inductors are greatly increased, resulting in poor efficiency under heavy-load conditions. To reduce total power losses and improve overall efficiency across the full load range, this article proposes a hybrid-mode modulation method based on carrier phase-shift control for a general two-parallel silicon carbide (SiC) converter, which enables adaptive and seamless switching between three operation modes, including soft-switching QCM, hard-switching continuous current mode (CCM), and no-switching CCM within one line cycle, according to the amplitude of the instantaneous phase current and reference signal. Comparative experiments conducted on a 600 V/12 kW two-parallel SiC converter prototype demonstrate that the proposed hybrid-mode method achieves the highest efficiency across the full-load range.

Achieving zero-voltage switching (ZVS) for parallel neutral-point-clamped (NPC) converters under high switching frequency and high power conditions is highly desirable for improving efficiency and power density, but remains challenging without auxiliary resonant circuits. In parallel converter systems, the circulating current between parallel legs provides an additional control degree of freedom that can be exploited to establish ZVS conditions. This paper proposes a software-based ZVS strategy based on variable phase-shift control for two-parallel T-type NPC converters. By actively regulating the circulating current between parallel legs, the inductor current is shaped into a quadrilateral waveform, enabling ZVS turn-on operation while maintaining a strictly constant switching frequency. Based on accurate prediction of the circulating current within one switching cycle, the phase-shift angle required to satisfy the ZVS condition over the line cycle is analytically derived. The proposed method effectively decouples the three phases and is applicable to both single-phase and three-phase systems. Experimental results obtained from a laboratory prototype validate the feasibility and effectiveness of the proposed strategy.

The widespread integration of distributed energy resources at the demand-side has facilitated the deep participation of prosumers in energy transactions, and gradually shifted traditional centralized trading to a semi-centralized peer-to-peer (P2P) trading mode. However, the inherent uncertainties in prosumer behaviors and the conflict of interest among prosumers pose significant challenges to P2P transactions. In this paper, a novel stochastic game-theoretic method for dynamic optimization of P2P transactions of prosumers. The Markov decision process in stochastic game is utilized to tackle the uncertainty in the behavior of prosumers, accompanied by the introduction of a novel method for calculating the state transition probability. To address the problem of “dimension explosion” of prosumers' states in the process of stochastic game, a more effective and reasonable adaptive state-tree reduction technology is employed for state selection. The existence of Nash equilibrium of stochastic game in the P2P trading among prosumers is proved by a clear mathematical approach, which establishes a theoretical basis for the practical application of stochastic game. Furthermore, a distributed algorithm for solving the trading strategies is proposed to preserve the privacy of prosumers. The simulation results compared with static game method prove the effectiveness of the constructed P2P transaction model based on stochastic game.

The efficient allocation of common energy storage (CES) resources within a community faces challenges due to complex, coupled constraints involving nonlinear power flow, local energy-sharing mechanisms, and uncertainties in load and photovoltaic (PV) output . To address these inherent complexities, this study formulates the problem as a nested generalized game (NGG) and proposes a semi-decentralized computational framework. The solution employs an extended Column and Constraint Generation (C&CG) algorithm, which decomposes the NGG into master and subproblems. Specifically, iterative algorithms are designed to solve these subproblems in parallel and sequentially, ensuring operational fairness and protecting participant privacy. Simulation results on a 10-bus community system and the IEEE 69-bus test system demonstrate the efficacy of the approach, confirming rapid convergence within limited iterations. The proposed scheme proves practical for real-world applications, balancing solution quality with critical advantages in privacy and fairness.

The accuracy of Universal Time (UT1) and Length of Day (LOD) forecasts can be improved by the z-component of short-term Earth effective angular momentum (EAM) forecasts. This study evaluates the accuracy of EAM forecasts from two key providers, German Research Centre for Geosciences (GFZ) and Eidgenossische Technische Hochschule Zürich (ETH), using Mean Absolute Error (MAE) on a comprehensive dataset spanning over 4 years. The results reveal different strengths. ETH’s forecasts are more stable, showing less impact from outliers in the mass terms of Atmospheric Angular Momentum (AAM) and Sea Level Angular Momentum (SLAM). With the original data, ETH’s accuracy was significantly higher across both 6-day and 10-day forecast lengths, outperforming GFZ by over 85

Zero-voltage-switching (ZVS) schemes are effective approaches for parallel converters to increase switching frequency, efficiency, and power density. However, existing ZVS methods based on variable switching frequency control face either a wide switching frequency range or excessive current ripples, resulting in high current stress and suboptimal efficiency. To address this issue, this article proposes a variable switching frequency phase shift pulse width modulation (VSF-PSPWM) for parallel converters. All switches operate in critical ZVS regions, thereby eliminating unnecessary current ripple. In the proposed VSF-PSPWM, the switching frequencies of three pairs of interleaved triangular carriers with 180 degrees phase difference are first synchronized and varied to shape the half-bridge (HB) currents into quadrilateral waveforms, creating sufficient ZVS conditions for all switches. Then, in over-ZVS regions, the 180 degrees is switched to a derived optimal phase shift angle to reduce the unnecessary current ripples. Meanwhile, the initial values of the carriers within each carrier cycle are modified to achieve positive and negative peak symmetry of the quadrilateral circulating current. Finally, experiments are conducted on a two-parallel SiC converter prototype to verify the effectiveness of the proposed method.

Grid-connected inverters play a crucial role in modern power systems with high penetration of renewable energy, where their dynamic behavior is influenced by multi-loop control structures, grid conditions, and nonlinear couplings. Conventional analysis methods fail to accurately characterize the nonlinear dynamic behavior of grid-connected inverters. In response to the aforementioned challenges, this paper investigates the system behavior under grid frequency disturbances and establishes a generalized nonlinear dynamic model. By employing perturbation methods, approximate analytical solutions of the system response are derived under three distinct types of frequency disturbances. Based on these solutions, three key nonlinear characteristics—frequency-dependent behavior, jump phenomena, and resonance effects—are systematically analyzed. The theoretical findings are further validated through experimental results.

Transient stability assessment (TSA) plays a crucial role in the analysis of power system. Owing to the large-scale integration of distributed energy resources (DERs), the resulting proliferation of inverters further exacerbates the nonlinearity and high dimensionality of power system. However, existing physics-driven methods often yield conservative results and involve high computational complexity, while learning based data-driven approaches suffer from limited interpretability. To address these challenges, this paper proposes a novel physics-informed deep learning framework to evaluate the transient stability of power system. First, an adjoint-based physics-dynamics learning (APDL) method is introduced to capture the transient behavior under arbitrary initial conditions. Next, leveraging these transient results, a Transformer-based multi-class classification model is developed to further identify the transient stability under various disturbances. Finally, the effectiveness and feasibility of the proposed method are validated through case studies on single machine infinite bus system, IEEE-39, bus system and WECC-240 bus system. The results suggest that, compared with the conventional PINN and data-driven approaches, the proposed method improves accuracy by 9.18% and 5.94%, respectively.

Large-scale grid integration of renewable generation is facilitated by resource abundance and advancements in power electronics. The high penetration of power electronics-based devices reduces system inertia, threatening grid stability. The Virtual Synchronous Generator (VSG) provides an effective solution. However, when the grid is unbalanced, problems such as unbalanced output current, overcurrent, and power fluctuations occur. Thus, a VSG power-current collaborative control strategy based on improved second-order generalized integrator (SOGI) is proposed. Firstly, the generation of power fluctuation and unbalanced current in VSG output under an unbalanced power grid is analyzed. Secondly, to suppress the DC component and high-order harmonics, an improved SOGI method is proposed for positive and negative sequence separation by introducing a difference node and adding an extra SOGI module on the basis of the traditional SOGI. To achieve the collaborative control of active/reactive power constant and current balance, a correlation coefficient mu is introduced and a unified equation is constructed. To prevent overcurrent during fault, virtual impedance and reactive power reference are introduced. Simulations have verified the effectiveness of the proposed method. It shows superiority in effective sequence separation, smooth power-current collaborative control, and safe operation without overcurrent.

This paper proposes a new method to depict the dynamic characteristics of hybrid AC/DC power distribution system with high-proportion renewable energy sources (RES), and describe its reachable regions under multiple uncertainties. By modeling multiple uncertainties based on zonotope and deriving differential-algebraic equations of the system, reachability analysis method for the hybrid AC/DC power distribution system is realized. The effectiveness of the proposed method are verified by comparing the results with Matlab/Simulink time-domain simulation and Monte Carlo simulation. It can obtain all possible reachable regions of the key state variables under uncertainty disturbances in one calculation, thus quickly determining the dynamic characteristics of the system without a lot of sampling calculations.

Modern high-penetration renewable grids host both grid-forming (GFM) inverters, which behave as voltage sources, and legacy grid-following (GFL) inverters, which inject phase-locked currents. Their coexistence creates a heterogeneous inverter-based resource (IBR) system whose mixed voltage−/current-source dynamics cannot be captured by classical synchronous-machine models or single-converter studies. This paper develops a unified analytical framework. A Kron-reduced nodal admittance model, merged with inverter control laws, is first transformed—via amplitude-domain averaging—into an explicit Lyapunov inequality that applies to any number of GFMs and GFLs. The inequality is condensed into a single scalar, the Unified-IBR Support Index (UISI). The controller term of UISI is strictly dissipative, whereas the network term quantifies real-time power exchange triggered by phase deviations; the sign of UISI alone certifies or refutes stability. Validation on a modified IEEE-9 benchmark (two GFMs, one GFL) shows that UISI pinpoints the transition between stable and unstable regimes and offers transparent tuning guidance for line reactance, virtual damping and GFL capacity. The proposed index therefore provides a computationally light yet physically interpretable tool for designing carbon-neutral grids dominated by heterogeneous IBRs.

Accurate forecasting of distributed photovoltaic generation is critical for grid operation, yet most existing models trained on data-rich sites exhibit poor generalization to heterogeneous and data-scarce PV plants. This motivates the development of a unified framework that can jointly deliver high-accuracy point forecasting, reliable uncertainty estimation, and strong generalization capability. Accordingly, a unified multi-objective framework (UPF) is proposed for distributed PV forecasting under limited-data conditions, enabling the joint optimization of deterministic point prediction and probabilistic interval estimation. The proposed UPF can be readily integrated with different base models for deterministic and probabilistic forecasting, offering strong transferability for ensemble optimization. To enhance physical consistency, three-dimensional PV geometric modeling is employed to construct enhanced solar-geometry features for improved cross-site generalization. In addition, a structure-preserving and risk-aware cross-site metric is developed to comprehensively assess forecasting robustness and generalization. Experiments on 36 globally distributed PV plants demonstrate that the proposed UPF method outperforms advanced baselines, achieving a 39.84% reduction in aggregated deterministic point-forecasting metric and 47.6% improvement in aggregated probabilistic interval forecasting performance

ABSTRACT One mainstream approach to alleviate insufficient voltage support in renewable‐energy power delivery systems is to introduce a portion of grid‐forming (GFM) inverters. However, the distinct characteristics of grid‐following (GFL) and grid‐forming (GFM) controls complicate the quantitative assessment of system stability capability. To address this issue, this paper proposes an amplitude mapping‐based method for quantitatively evaluating stability capability, yielding a simple and practical analytical expression. Specifically, we introduce the idea of assessing system stability through waveform‐amplitude stability. Based on this concept, the mathematical model of the renewable‐energy delivery system is established, and the expression of the stability capability index (SA) is derived. Next, the impacts of key parameters on SA are analysed, and the critical GFL–GFM power ratio is quantified. Finally, the theoretical findings are validated through case studies.

Accurate forecasting of distributed photovoltaic (PV) power generation is vital for grid stability and efficient energy management. While recent advances in machine learning have improved PV power prediction, most models overlook physical mechanism features, resulting in black-box behavior with limited interpretability and only marginal gains in forecasting accuracy. To address these limitations, this paper proposes an interpretable ensemble learning framework augmented with physical information. A physically constrained surface for PV power generation is first constructed based on astronomical angles and irradiance-related features. This surface is incorporated into the deep learning training process by modifying the loss function, allowing physical priors to guide model learning and enhance interpretability. Building on this, an interpretable ensemble learning framework is developed by integrating a Kolmogorov–Arnold theory-based physical predictor with conventional machine learning models, leveraging the complementary strengths of these models to improve prediction accuracy and generalizability. To further enhance model transparency, the SHapley Additive exPlanations method is employed for feature attribution, providing insights into the contribution of input variables to the model output. Case studies conducted across 55 distributed PV stations demonstrate that incorporating physical-angle features enhances forecasting accuracy by 0.4%–1.37% on average. In data-scarce scenarios, models augmented with physical priors exhibit clear performance advantages. Overall, the proposed physically-informed ensemble model achieves superior generalization capability and consistently outperforms baseline methods such as LightGBM and MLP, yielding an average accuracy improvement of 0.38%–2.03%.

With the increasing penetration of renewable energy, power systems are transitioning from synchronous-machine-dominated to converter-dominated operation. Grid-forming converters (GFMs) are expected to establish voltage references and support system stability. Conventional droop control, which couples active power with frequency and reactive power with voltage, can limit voltage support and aggravate control interactions under high-load conditions.This paper focuses on reactive power regulation in voltage-oriented constant-frequency GFM systems and proposes a Q–Us droop control strategy. In the proposed scheme, the active power–frequency channel is removed, and the converter operates as a fixed-frequency voltage source. Reactive power is regulated by adjusting the voltage magnitude, making the Q–Us droop coefficient both a reactive power control parameter and an indicator of the converter's equivalent voltage stiffness.The coordination between GFMs and the synchronous machine is further examined. GFMs respond rapidly to voltage disturbances and provide transient reactive power support, while the synchronous machine gradually supplies steady-state reactive power through its excitation system, reducing the continuous current burden of the converters and preserving their regulation margin.

With the continual integration of vast amounts of renewable energy into power systems, its transient stability assessment (TSA) has become increasingly critical. Traditional model-driven approaches suffer from slow computation and excessive conservatism, while existing data-driven methods often exhibit poor interpretability and limited accuracy. To address these challenges, we propose a transient stability assessment method for power systems based on the Koopman neural operator. Leveraging Koopman operator theory, our approach employs a deep neural network to adaptively learn the mapping function that linearizes the nonlinear dynamics of power systems. Building on this linear representation, we further utilize a temporal convolutional network (TCN) to capture transient sequential data, enabling rapid stability discrimination under arbitrary disturbances. Finally, we validate the effectiveness and feasibility of the proposed method on both the single-machine infinite-bus system and the IEEE 9-bus test system.

With the advancement of power electronics technology, converters achieve compactness and high power density by increasing switching frequency and reducing passive components. However, this compromises the filtering capability to suppress high-frequency harmonics and intensifies high-frequency resonance issues in multi-machine interconnected systems. The problem becomes even more complex in grid-following (GFL) and grid-forming (GFM) converter interconnected systems due to their distinct dynamic characteristics. Traditional active damping methods fail to effectively mitigate such high-frequency resonances. For GFL converters, this paper investigates the interaction mechanisms between various active damping techniques and high-frequency harmonics, and proposes a virtual-filter-based active damping method that feeds back capacitor voltage through a quasi-resonant controller. This approach effectively suppresses high-frequency resonance, maintains high control bandwidth, and avoids the drawback of conventional capacitor-voltage feedforward, which tends to amplify high-frequency disturbances. For GFL-GFM interconnected systems, the paper further analyzes how different active damping strategies affect system damping characteristics and the interaction between GFL and GFM converters, leading to a rational active damping configuration. The proposed scheme successfully suppresses high-frequency resonance while preserving fast dynamic response, with experimental results confirming its effectiveness and feasibility.

Research on time and frequency transfer between stations through Global Navigation Satellite System (GNSS) carrier-phase observation data has been a hot topic for many years. However, the estimation of ambiguity has always been a challenge. Unlike Global Positioning System (GPS), BeiDou System (BDS) is a hybrid constellation with GEOstationary (GEO) satellites included. By virtue of the stationary characteristics of BDS GEO satellites, a method of precise common-view time and frequency transfer is proposed in this paper. With this method, highprecision time and frequency transfer can be achieved by utilizing carrier-phase observation data from BDS GEO satellites and the precise products of the International GNSS Monitoring and Assessment System (iGMAS). Unlike traditional GNSS Medium Earth Orbit (MEO) satellites, BDS GEO satellites offer continuous visibility within their coverage areas (mainly in the Asia-Pacific region), enabling a single ambiguity to be maintained over extended periods, up to 26 days in our experiments, which can be calibrated as a systematic error. Additionally, the phase wind-up effect becomes a stable bias that can be calibrated as part of the systematic error. With sites in Europe and China, experiments based on this method are performed, and the results show that: 1) For zero and ultrashort baselines, the Root Mean Square (RMS) values of the proposed method are better than 0.1 ns; 2) For the short baseline (33 km), the RMS value of the difference between the proposed method and Two Way Optical Time and Frequency Transfer is 0.28 ns; 3) For the long baseline (700 km and 1750 km), the performance of the proposed method is compared against Two Way Satellite Time and Frequency Transfer, showing competitive RMS values and superior frequency stability; 4) For inter-continental baselines (over 7000 km), the RMS value of the residuals with respect to Precise Point Positioning time transfer is at the sub-nanosecond level.

How to achieve urban power restoration with the help of microgrid (MG) in the face of natural disasters has become a research hotspot. This paper aims to research a flexible interconnection method to enhance power supply capacity. First, a flexible DC interconnection method covering a large spatial area is proposed. Then, based on a modular modeling method for high order systems considering interaction characteristics of Voltage Source Converter (VSC) ports, an interconnection selection method is built to compare the power supply performance of system under star structure and hand-in-hand structure. Furthermore, a dynamic adjustment strategy based on control mode is formed. Finally, the corresponding simulation and experimental verification shows that the proposed method is able to obtain optimal structure and master station to get the maximum power supply capability, while still ensuring high reliability in the face of secondary disasters.