Small-signal stability analysis of offshore wind power integration typically relies on impedance-based methods; however, traditional manual approaches are highly inefficient when applied to complex systems. Inspired by the companion-circuit representation and nodal-analysis framework used in the electromagnetic transients program (EMTP), this paper proposes a companion-circuit-based automated impedance modeling method for small-signal stability analysis. The method discretizes component dynamics through the companion circuit representation and constructs system-level models based on nodal analysis. Subsequently, the z-transform and bilinear transform are applied to convert the system-level port-equivalent discrete-time (DT) model into a continuous-frequency impedance model. The proposed method can be fully automated in a computer environment, enabling efficient computation of the impedance and small-signal stability analysis of offshore wind farm integrated via fractional frequency transmission system (FFTS), and providing a general computational framework for impedance modeling and small-signal stability analysis of complex power electronic systems.
This paper presents new closed-form expressions for the calculation of earth-return parameters of submarine cables, explicitly accounting for three-medium environments consisting of air, seawater, and seabed. Configuration-specific closed-form expressions are derived for cables located at the sea-seabed interface and for cables buried in the seabed, overcoming the inherent limitations of conventional two-medium representations. The proposed expressions are validated against rigorous three-layer reference solutions and are also compared with existing two-medium approaches. Numerical results demonstrate very good agreement with the three-layer reference model over a wide frequency range, with particularly improved accuracy at higher frequencies where earth-return effects dominate. Although two-medium approximations generally introduce modest deviations, the proposed closed-form expressions further reduce these discrepancies in a systematic manner. Owing to their analytical nature and computational efficiency, the proposed formulations provide a practical, robust and physically consistent tool for electromagnetic transient analysis of offshore and submarine cable systems.
While arm multiplexing technology significantly enhances the power density of MMC, it also compromises the inherent energy buffering capability. This paper focuses on a specific implementation of this technology: the Single-Arm Multiplexed MMC (SAM-MMC), a representative full-time multiplexing topology that may achieve the most compact design. Due to the lack of internal energy buffering, it experiences uneven energy accumulation during asymmetric faults, resulting in capacitor energy impact and inter-phase imbalance. To address this issue, this paper proposes a cost-effective strategy with Virtual-Impedance-Based Inter-Phase Energy Balancing (VIB). The core idea is to emulate a controllable virtual impedance by dynamically adjusting each phase's commutation angle, thereby compensating for unbalanced energy distribution without extra hardware. First, a sequence‑component model of the SAM‑MMC under asymmetrical faults is established to clarify the energy imbalance mechanisms. A cooperative control framework is then developed, integrating feedforward decoupling suppression of negative-sequence currents with dynamic inter-phase energy redistribution for embedded autonomous energy balancing. Simulation results demonstrate that the proposed strategy effectively maintains balanced three-phase currents and prevents switch overcurrent. Furthermore, HIL experiments validate the feasibility of the approach. Therefore, the proposed energy balancing method provides a reliable solution for enhancing fault ride-through capability of the compact MMC-HVDC for large-scale wind power integration.
The X-ray radiation generated by vacuum interrupters (VIs) has become a subject of growing scientific and engineering concern due to possible cumulative radiation damage to adjacent equipment and human health. In high-voltage VIs, the operational X-ray irradiation dose on ceramic components can reach the order of Sieverts (Sv), potentially inducing significant surface charge accumulation. This study investigates the effects of X-ray irradiation on surface charge characteristics of alumina ceramics, focusing on the interplay between radiation dose and surface roughness. An integrated experimental platform combining isothermal surface potential decay (ISPD) measurements with X-ray irradiation was developed to measure and analyze X-ray-induced charge dynamics under vacuum conditions with the active electrostatic probe method. Results revealed that X-ray exposure modifies trap parameters, increasing both shallow and deep trap levels and densities, which retards surface charge decay. A critical surface roughness threshold of approximately 2 μm is identified, which is valid for the X‑ray energy spectrum used in this study (peak at ∼90 keV, ranging from 50 to 270 keV). For higher X‑ray energies, the threshold roughness becomes significantly larger. Below this value, smoother surfaces facilitated photon penetration and electron emission, leading to higher charge accumulation, while rougher surfaces exhibited charge density saturation due to enhanced electron trapping and recombination. The study provides insights into optimizing ceramic insulators for high-voltage equipment by balancing surface roughness to minimize radiation-induced charge accumulation, enhancing operational reliability in radiation-prone environments.
The secure performance of the distance relay in the presence of power swings is still taken into consideration as one of the most important concerns in the field of protection. This study introduces a novel method for extracting modulated current and voltage signals under power swing conditions to enable symmetrical fault detection. The kernel is based on transferring voltage and current signals from the stationary $abc$ reference frame into the $\alpha \beta$ reference frame. The method would help convert a modulated sinusoidal signal to a simple sinusoidal one. The $\alpha \beta$ reference frame based on the proposed method is fast and mathematically simple and it can be implemented with practical ease. The effectiveness of the developed method is assessed through simulation in two sample systems; i.e., the single-machine to infinite bus (SMIB) and the New England 39-bus systems. Multiple simulation scenarios involving fault location, fault initiation time, and fault resistance under slow, moderate, and fast power swing conditions, are conducted to examine the effectiveness of the proposed method.
DC auto-transformer (DCAT) based traction power supply system offers significant advantages in mitigating both the stray current and rail potential issues in urban rail transit. Each DCAT employs the voltage-balancing circuit (VBC) to maintain voltage equilibrium within the traction network. However, the conventional DCAT lacks adequate fault-tolerant capability, as either internal device faults or traction network faults easily lead to fault propagation and critical component damage of DCAT. To address this issue, this paper proposes a fault-tolerant DC auto-transformer (FT-DCAT) with enhanced protection scheme. Compared to conventional DCAT, the proposed FT-DCAT adds a fault protection circuit to control traction network connectivity and employs multiple improved VBCs for the redundant energy transfer. Firstly, the topology and principle of FT-DCAT are analyzed, including its three typical conditions: normal condition, redundant condition, and fault isolation condition. Then the fault mechanisms and corresponding protection schemes are discussed for internal device faults and traction network faults. And the stray current and rail potential mitigation performance of FT-DCAT system after isolating the faulty unit are evaluated. Finally, the simulation and experimental results validate the effectiveness of proposed protection scheme for FT-DCAT system.
Wildfires pose a severe external threat to overhead lines and can induce transient faults that may subsequently develop into permanent faults. Therefore, timely detection of wildfire-induced transient faults is crucial to prevent their progression and to enable prompt mitigation measures that minimize service interruptions. Existing WOLF detection methods generally rely either on expert-defined features or on purely data-driven models. Expert-based methods have limited adaptability to complex power systems and diverse fault conditions, whereas data-driven models are sensitive to the quantity and quality of labeled data. To address these issues, a fault mechanism-based WOLF detection method is proposed. First, a robust WOLF detection indicator based on physical parameters of fault branches is presented. Then, an Arc-Discharge Physics-Informed Neural Network (AD-PINN) is developed, which incorporates arc-discharge physics constraints into the learning process to overcome the challenges of limited fault samples and incomplete equivalent physical modeling in computing the WOLF detection indicator. Lastly, to prevent gradient imbalance and training divergence caused by overly random parameter initialization in the early training stage, a domain knowledge based initialization strategy is established. Validation through multiple experimental scenarios demonstrates that the proposed method outperforms existing methods and exhibits stable performance in different fault scenarios, achieving an overall accuracy of 93.75% despite label inaccuracies and limited data.
Conventional power swing detection schemes generally rely on the assumption that the apparent impedance trajectory observed by a distance relay varies slowly and continuously during a power swing. However, this assumption may no longer hold when a grid-forming (GFM) inverter-based resource (IBR) enters current saturation. This paper theoretically derives the conditions for entering and exiting current saturation under circular, d-axis priority, and q-axis priority current saturation algorithms (CSAs), and analyses the corresponding full-cycle apparent impedance trajectories. The analysis reveals that the CSAs fundamentally reshape the impedance trajectories observed by protective relays, leading to behaviours that are qualitatively different from those of synchronous generator (SG)-based systems. Moreover, it is demonstrated that the conventional power swing detection scheme may lose functionality due to the rapid movement of the trajectory. To mitigate this issue, a current vector angle holding strategy is proposed to maintain the continuity of the apparent impedance trajectory during the transition into current saturation. The theoretical findings and the effectiveness of the proposed strategy are validated through MATLAB/Simulink simulations using a simplified grid-connected GFM IBR system and a modified IEEE 9-bus system.
Transformers are critical equipment in power systems that often experience internal or external short circuits (SC), which electromechanically stress the windings. Even minor, localized internal SC can alter the winding's electromagnetic properties, which can subsequently cause mechanical deformations and, if left unaddressed, eventually escalate into catastrophic failures. Detecting such conditions at their inception is paramount to achieving higher system reliability. One of the most sensitive monitoring methods for detecting such conditions is frequency response analysis (FRA). Even after four decades of existence, the interpretation of FRA data still poses multiple challenges and remains a grey area. Motivated by this, the present article seeks to understand how FRA signatures are affected by a localized internal SC in the winding. For this purpose, an experimental setup comprising a single 33 kV, 3.5 MVA isolated continuous-disc winding was assembled. A controlled localized SC across one double-disc ($\approx$4.5% of winding length) was introduced sequentially at various positions, and at each step, FRA data were recorded. Then, peaks and troughs were extracted, and their variations were examined along with variations in the FRA signature, computed high-frequency inductance of winding, and several statistical indices. Thereafter, a single turn-to-turn level SC experiment was conducted. A distinct, abrupt change was observed in the FRA magnitude response measured for different SC locations.
This paper presents a quasi-distributed Fiber Bragg Grating (FBG) sensing system integrated with machine learning for differentiated estimation of icing loads on overhead conductors and composite insulators. We designed a 10 kV unenergized insulator sensor featuring twelve interface-embedded and one tail embedded FBGs. To address the coupled responses of conductor and shed icing, a two-stage response-separation procedure is adopted: conductor icing is first estimated using the ceramic packaged FBG, and its influence on the shed FBG channels is subsequently compensated before regional shed icing loads are inverted using existing regression models. An Extreme Learning Machine (ELM) model predicts conductor icing with a 14.60% relative error, while a Least Squares Boosting (LSBoost) model assesses multi-point shed icing, with relative errors of 4.1% and 0.8% for the two monitored sheds. A natural-icing case study at the Guizhou Ice Observation Station provides preliminary evidence of the feasibility of the proposed sensing and inversion workflow under the tested conditions.
Accurate time synchronization is a prerequisite for pilot differential protection in power systems. Existing synchronization methods either rely on external references such as global positioning system (GPS), which are vulnerable to signal loss and cyber attacks, or require additional communication channels, which increase system cost and complexity. To address these limitations, this paper proposes a two-stage self-synchronization scheme that achieves high accuracy using only electrical measurements. The method first exploits the initial traveling waves generated by a fault and then refines the result with steady-state phasor information, thereby ensuring robustness against various non-ideal conditions. Theoretical derivation proves its validity, and extensive PSCAD/EMTDC simulations, hardware experiments, and a field fault record confirm its effectiveness under different fault scenarios, parameter uncertainties, frequency deviations, and noise disturbances. The results demonstrate that the proposed approach can achieve synchronization errors well within acceptable limits, making it a promising solution for practical deployment in power system protection.
Lightning-induced transients pose a significant threat to buried cables and connected equipment, yet the influence of strike locations on cable response remains insufficiently supported by experimental evidence. This paper presents rocket triggered lightning experiments to investigate the transient behavior of a 20-m buried armored four-core cable during return stroke stages. Measurements were obtained for three representative strike locations: the main grounding grid, an extended grid, and a remote earth point. The recorded voltage waveforms were analyzed in terms of amplitude, polarity, rise time, duration, half-peak width, and specific energy. Results show that cable response is strongly dependent on strike location. Peak voltages are substantially higher for grid-connected strikes (227 1214 V) than for remote-earth strikes (7–35 V), with the largest amplitudes observed at the main grounding grid. Under the negative return stroke analyzed in this study, the measured voltage polarity also varies with strike location, being predominantly positive at the main grid and remote earth but mainly negative at the extended grid. Remote-earth strikes exhibit longer rise times but shorter durations compared with grid-connected strikes, while the half-peak width remains relatively constant (2–6 μs). Moreover, the specific energy of induced voltage by remote-earth strikes is nearly three orders of magnitude lower than that at grid connected locations. The experimental dataset provides field evidence for evaluating strike-location-dependent trends and offers reference data for future model development and validation.
Transmission and distribution systems are vulnerable to extreme weather events. This vulnerability is evident in the growing frequency of faults caused by lightning strikes, direct contact with trees, and equipment failures. Moreover, the growing power demand forces electrical system equipment to operate beyond its rated capacities. Consequently, reclosers and transformers in the substations are experiencing overstress. In this context, this work presents the tests of a developed Solid-State Fault Current Limiter (SS-FCL) for installation in a medium voltage distribution substation. The developed equipment is composed of the solid-state switch with insulated-gate bipolar transistors (IGBTs), the maneuver and protection cubicle, and air core reactors. As it is equipment that involves software and hardware, it is necessary to mitigate errors in the coordination of the equipment for safe operation. In preparation for future testing in medium-voltage, this research focuses first on troubleshooting the proposed solid-state system at reduced voltage (220 V). The following tests were carried out at the equipment manufacturer's facilities: hardware tests (Intermittent test and Open switch test) and software tests or detection tests (Load switching test, single-phase and three-phase short-circuit test with and without downstream impedance). The goals of these tests are to analyze the performance of the computational algorithm in the detection of the short circuit and evaluate the supportability of the solid-state switches in terms of voltage and current. These tests validate the equipment for the medium-voltage test stage, which will be the next step of this work.
In converter-dominated grids, the earliest post-fault interval is often limited by operating-quantity extraction, because cycle-based discrete Fourier transform (DFT) phasors can incur finite-window bias under fast control actions, current limiting, and waveform distortion. This paper develops a trajectory based, sub-cycle operating-quantity extractor that acts directly on instantaneous three-phase measurements. Leveraging the recently proposed concept of geometric frequency (GF) and using short-window least-squares differentiation, the proposed method separates the instantaneous stretching and rotation of the three phase trajectory and converts them into a closed-form equivalent series R–L drop. Resulting parameters are mapped onto the conventional R–X plane to drive standard mho and quadrilateral logic. A memory-polarized directional torque is also formed from instantaneous three-phase vectors to maintain sign consistency under voltage depression while reducing cycle-length reporting latency. Electromagnetic transient (EMT) case studies on a wind farm export corridor and real-time digital simulator (RTDS) based validation on a modified IEEE 9-bus transmission system verify the effectiveness of the proposed GF-based distance and directional protection method.
Accurately calculating the scattered electric field from transmission lines is the prerequisite for formulating passive interference suppression measures. Limited by the operating memory of hardware devices, existing calculation method is only applicable to frequencies of 30 MHz and below. To address this, this paper proposes a sub-region solution algorithm for calculating the scattered electric field from transmission lines. This algorithm divides the entire integral domain of the transmission lines into several sub regions, and the initial induced current generated by each sub region and the coupled induced current generated by electromagnetic coupling between sub regions are independently calculated. A matrix equation for the weighting coefficients of these initial and coupled induced currents is constructed and solved, and the final induced current and the scattered electric field generated on the surface of the transmission lines are obtained. This avoids the exponential increase in computational complexity during the global solution of transmission lines integration when the number of mesh sections is too large, and achieves accurate solution of the scattered electric field from transmission lines in very high frequency band (30–300 MHz). Computational results demonstrate that under excitation by a 300 MHz electromagnetic wave, the proposed algorithm consumes less than one-fourth the operating memory and less than 35% of the computation time required by the MoM method, the calculation deviation from the MoM method is 5.01%, which is 47.79% higher than the traditional IPO method.
With the integration of large-scale offshore wind power, both the inertia and damping of the onshore power grid exhibit a significant decreasing trend. The onshore modular multilevel converter (MMC) station typically adopts constant DC voltage control to maintain the power balance of the DC system, which makes it difficult to provide inertia to the onshore AC grid. To achieve both DC voltage regulation and AC grid support, existing research has proposed matching control, which relies on DC-link voltage for synchronization and leads to significant DC-link voltage perturbations during frequency disturbances. To address the problem, this paper proposes a novel capacitor energy-based hybrid synchronization (CEHS) control. Compared with the existing dual grid-forming control, the proposed CEHS control achieves dual grid-forming while operating robustly under a wide range of short-circuit ratios (SCRs) for the onshore AC grid. Furthermore, this paper establishes an accurate sequence impedance model of the CEHS control and analyzes the impact of core parameters and SCR on the small-signal stability. Finally, the effectiveness of the proposed CEHS control and the corresponding parameter design methodology is validated in PSCAD/EMTDC.
In power distribution systems with multiple time-varying harmonic sources, to address the limitation in the accuracy of harmonic power flow (HPF) calculations due to the difficulty in accurately obtaining harmonic source and system models, this paper proposes a high-accuracy time-varying probabilistic harmonic power flow (PHPF) calculation method based on iterative correction of the harmonic coupling matrix model (HCMM). First, the harmonic-coupled HPF equation of the system is established. Second, the HCMM is iteratively corrected using time-series measurements of node voltages and currents, and adaptive time-segmentation is performed according to the variation characteristics of harmonic source voltages and currents. Finally, to overcome the limitations of the independence assumption and symmetric distribution assumption, the point estimation method is improved based on Nataf–Cholesky transform decoupling and asymmetric sampling, achieving high-accuracy PHPF calculation. In the IEEE-33 and IEEE-123 bus test systems, the relative errors of voltage total harmonic distortion obtained by the proposed method are below 1%, significantly better than the traditional PHPF calculation method (about 10%), with an accuracy improvement of about 10 times. In addition, the actual distribution system is used to verify the performance of the proposed method.
Harmonic coupling and the stability of modular multilevel converters (MMCs) have been extensively studied under balanced conditions. However, in practical applications, MMCs may operate under unbalanced conditions due to fac-tors such as faults and protection actions. This paper investi-gates the harmonic coupling and stability of MMC under sin-gle-phase disconnection (SPD) conditions, a scenario that, to the best of the authors' knowledge, has been relatively under-explored in the existing literature. To address this gap, the paper develops a comprehensive harmonic state-space model for an MMC-HVDC system under SPD condition. Using this model, a multi-input multi-output harmonic coupling matrix is derived to analyze the interactions between different harmon-ics and the signal-flow graph is depicted to explain the mech-anisms behind these couplings. Furthermore, the multi-input multi-output matrix is transformed into a single-input single-output impedance that encapsulates all harmonic couplings, thereby enabling the visualization of the effects of various couplings on system stability through impedance variations. Nyquist curve based stability analysis, along with the hard-ware-in-the-loop experiments, underscores the importance of incorporating SPD conditions in the parameter design of MMC-HVDC systems.
The classification of fault types in inverter-based resource (IBR) plants has become important for proper operation. However, recent methods have been developed for relays installed at the point of measurement, whereas IBR units operate based on point of connection (POC) measurements. There, typical IBR plant transformer configurations render zero-sequence quantities unavailable and may shift sequence-component phases, thereby precluding direct application of these methods. In light of this, this letter proposes a fault type classification scheme applicable at the POC. By considering the practical IBR plant structure, the scheme extracts the phase difference between the negative- and positive-sequence currents at the fault point and, accordingly, identifies the faulted phase(s). An additional criterion is then introduced to discriminate between line-to-line and line-to-line-to-ground faults. Extensive PSCAD simulations demonstrate the accuracy, speed, and high reliability of the proposed scheme for control and operational applications.
