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Search Results (208)

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Keywords = phasor measurement unit (PMU)

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33 pages, 1775 KB  
Article
Frequency Control Capability Estimation for Renewable Energy Stations Accounting for Dynamic Response Variations and Power Decoupling
by Zhihui Tong, Zhirong Li, Xu Jing, Weishang Meng and Jiayu Li
Eng 2026, 7(7), 323; https://doi.org/10.3390/eng7070323 - 2 Jul 2026
Viewed by 84
Abstract
The large-scale integration of converter-interfaced renewable energy sources has significantly reduced power system inertia, posing challenges to frequency stability. Although virtual inertia and primary frequency control can enhance the frequency support capability of renewable energy units, their actual performance often deviates from set [...] Read more.
The large-scale integration of converter-interfaced renewable energy sources has significantly reduced power system inertia, posing challenges to frequency stability. Although virtual inertia and primary frequency control can enhance the frequency support capability of renewable energy units, their actual performance often deviates from set values due to dynamic response differences among various energy sources (e.g., energy storage, photovoltaic, and wind power) and coupling between inertia and primary regulation power. Existing evaluation methods fail to accurately decouple these components or account for unit-specific dynamic characteristics, leading to considerable estimation errors. To address these issues, this paper proposes a novel estimation method for the frequency regulation capability of renewable energy stations. First, the dynamic frequency response characteristics of synchronous and renewable generators are compared. Then, a decoupling method is developed to separate virtual inertia power from primary frequency regulation power by leveraging their distinct response features. A first-order plus delay time (FOPDT) model is employed to characterize the external frequency response of different renewable energy units. The primary frequency regulation coefficient is estimated using a sliding window integration method, and the virtual inertia time constant is identified via a gradient descent algorithm based on the decoupled inertia power. A hardware-in-the-loop experimental platform is constructed using a real-time digital simulator (RTDS) and phasor measurement units (PMUs) to validate the proposed method. Simulation results show that the estimation errors for energy storage, photovoltaic, and wind power units are 0.63%, 6.38%, and 8.38% for the virtual inertia time constant and 0.45%, 0.72%, and 3.81% for the primary frequency regulation coefficient, respectively. Field test data further confirm the practical applicability and accuracy of the approach. The proposed method enables precise frequency control capability estimation, providing a reliable basis for parameter setting and capacity configuration of frequency regulation resources in low-inertia power systems. Full article
(This article belongs to the Section Electrical and Electronic Engineering)
21 pages, 10030 KB  
Article
Architecture of an Edge Processing System for Aggregated Generation of PhotoVoltaic Plants with Expanded PMUs
by Victor Pallares-Lopez, Juan Jose Gonzalez-de-la-Rosa, Agustin Aguera-Perez, Rafael Real-Calvo, Miguel Gonzalez-Redondo, Isabel Santiago-Chiquero, Manuel Jesus Espinosa-Gavira, Olivia Florencias-Oliveros, Jose Maria Sierra-Fernandez, Jose Carlos Palomares-Salas and Victoria Arenas-Ramos
Energies 2026, 19(12), 2827; https://doi.org/10.3390/en19122827 - 13 Jun 2026
Viewed by 369
Abstract
Currently, there is a trend in the energy sector towards the application of edge computing techniques to facilitate active monitoring of distribution networks. The adoption of this technique is crucial for applications involving distributed monitoring systems that require real-time data processing with low [...] Read more.
Currently, there is a trend in the energy sector towards the application of edge computing techniques to facilitate active monitoring of distribution networks. The adoption of this technique is crucial for applications involving distributed monitoring systems that require real-time data processing with low latency. An edge computing environment ensures an adequate response to two time-level response requirements. One for events that could trigger a serious problem in the distribution network, and a less demanding one for the management of energy. This article justifies and analyzes an architecture specifically designed to provide an adequate response to the two levels of time demand that set the procedure followed for the monitoring, storage and local diagnosis of several photovoltaic plants located on the same distribution network, with the aim of studying their joint production. One of the main contributions is related to the expansion of the capabilities of Phasor Measurement Units (PMUs) to monitor solar radiation or energy production perimeters by sector. The second major contribution is to guarantee the quality of the measurements and low latency in communications, using as a reference the IEEE C37.118-2011 synchrophasor standard in cooperation with the Time Sensitive Networking (TSN) synchronization protocol that guarantees simultaneity in distributed measurements. In short, a procedure is sought that allows a real-time response with the use of computing techniques very close to the origin of the measurements, guaranteeing exhaustive control from the moment the capture begins until the parameters are stored in a time series database. Full article
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29 pages, 6014 KB  
Article
Parameters Identification of Sub-Synchronous Oscillation in D-PMSG Based on Improved VMD and TLS-MP
by Hanbo Wang, Guoxian Guo, Yantao Wang, Hongbin Li, Bing Liu, Yingwei Wang and Minghui Li
Electronics 2026, 15(11), 2342; https://doi.org/10.3390/electronics15112342 - 28 May 2026
Viewed by 233
Abstract
To address the problems of modal aliasing, limited identification accuracy, and inadequate noise adaptability in the parameters identification of sub-synchronous oscillation (SSO) in direct-drive permanent magnet synchronous generator (D-PMSG), a method based on improved variational mode decomposition (VMD) and total least squares matrix [...] Read more.
To address the problems of modal aliasing, limited identification accuracy, and inadequate noise adaptability in the parameters identification of sub-synchronous oscillation (SSO) in direct-drive permanent magnet synchronous generator (D-PMSG), a method based on improved variational mode decomposition (VMD) and total least squares matrix pencil (TLS-MP) is proposed. The grid-connected current of the D-PMSG, acquired by the phasor measurement unit (PMU), is decomposed through VMD, which is optimized via the Bayesian optimization (BO) algorithm to determine the optimal number of intrinsic mode functions (IMFs) K and the penalty factor α. By this means, mode mixing phenomena in VMD are eliminated, and noise adaptability is reinforced. The derived IMFs are subjected to mutual information (MI) analysis with the grid-connected current, from which the dominant IMFs are extracted. Each dominant IMF is subsequently resampled, and its parameters are identified through TLS-MP. In this process, the strength Pareto evolutionary algorithm II (SPEA2) is employed to improve the MP method, and the optimal signal subspace order g is obtained, which facilitates improved identification accuracy and noise adaptability. Finally, TLS is incorporated to accomplish the identification of characteristic parameters of the D-PMSG SSO components, including amplitude, frequency, phase, and damping factor. Simulation analyses based on composite signals and a four-machine two-area system model containing a direct-drive wind farm are conducted, and the effectiveness of the proposed identification method is validated. Full article
(This article belongs to the Section Power Electronics)
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31 pages, 8650 KB  
Article
Distribution Network Fault Location Method Based on Limited Measurement Information
by Kui Chen, Wen Xu, Yizhi Liu, Yuheng Yang and Wenhao Zhu
Electronics 2026, 15(10), 2044; https://doi.org/10.3390/electronics15102044 - 11 May 2026
Viewed by 272
Abstract
Due to the complex structure and large number of nodes in distribution networks, it is difficult to achieve full coverage of synchronous phasor measurement units (μPMUs) in actual engineering projects, resulting in limited available measurement data. To address this issue, this paper proposes [...] Read more.
Due to the complex structure and large number of nodes in distribution networks, it is difficult to achieve full coverage of synchronous phasor measurement units (μPMUs) in actual engineering projects, resulting in limited available measurement data. To address this issue, this paper proposes a distribution network fault location method based on limited measurement information. First, the distribution characteristics of the node positive-sequence voltage measurement deviation (NPSVMD) following a fault occurrence are analyzed. On this basis, a principle for faulted line identification is established by exploiting the common-path property between the measurement point exhibiting the maximum NPSVMD and the reference node. Furthermore, the fault current is equivalently derived using the nodal voltage variation equations (NVVE), and a distance estimation function is constructed by incorporating the NPSVMD values at the measurement nodes on both sides of the faulted line, thereby enabling accurate determination of the fault location. Simulations on the IEEE 33-bus distribution system verify that the proposed method can accurately identify the faulted line and achieve high-precision distance estimation using limited measurement information, demonstrating strong robustness and superior adaptability. Full article
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22 pages, 2243 KB  
Article
Time Synchronization Attack Detection Method Based on Carrier Doppler Pearson Correlation Coefficient Estimation
by Lifen Li and Zhiyun Xiao
Sensors 2026, 26(9), 2811; https://doi.org/10.3390/s26092811 - 30 Apr 2026
Viewed by 700
Abstract
The global navigation satellite system (GNSS), the main time synchronization method for phasor measurement units (PMUs) in smart grids, is highly vulnerable to time synchronization attacks (TSAs). This affects the timing of results and poses a serious threat to the safe and stable [...] Read more.
The global navigation satellite system (GNSS), the main time synchronization method for phasor measurement units (PMUs) in smart grids, is highly vulnerable to time synchronization attacks (TSAs). This affects the timing of results and poses a serious threat to the safe and stable operation of power systems. To quickly detect TSAs and minimize the impact of time errors on PMU sensor networks, a TSA detection method based on carrier Doppler Pearson correlation coefficient estimation is proposed. This method can be directly implemented on existing commercial receivers without modifications. The method leverages the fact that carrier Doppler shifts in each satellite channel exhibit consistent changes when subjected to a TSA; therefore, if there is a correlation between channels, a consistent change in carrier Doppler shift caused by the TSA can be quickly detected through Pearson correlation coefficient estimation. In the TSA detection experiment, the proposed method was compared against four existing TSA detection methods on a self-developed experimental platform. The experimental results show that compared with the other four methods, the proposed method responds 4–22 s faster and has better detection speed, with more significant changes in the detection statistics. Notably, these advantages become more pronounced as the spoofing speed decreases and the spoofing stealthiness increases, indicating that this method has robust detection capability against sophisticated attacks. Meanwhile, it offers a lightweight computational overhead suitable for embedded PMU implementations, enhancing sensor-layer security in critical infrastructure. This work provides reliable synchronized measurements for power system monitoring and control over a wide area. Full article
(This article belongs to the Section Industrial Sensors)
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27 pages, 4042 KB  
Review
Applications of Distribution Phasor Measurement Units for the Integration of Distributed Energy Resources in Modern Distribution Networks
by John Steven Fierro-Rincón, Carlos Arturo Lozano-Moncada, Eduardo Gómez-Luna, Luis Fernando Grisales-Noreña and Daniel Sanin-Villa
Appl. Syst. Innov. 2026, 9(5), 92; https://doi.org/10.3390/asi9050092 - 29 Apr 2026
Cited by 1 | Viewed by 1506
Abstract
The rapid growth of Distributed Energy Resources (DERs) has intensified operational challenges in modern distribution networks, especially with respect to observability, bidirectional power flow, feeder model accuracy, and fast event detection. This review critically examines the role of Distribution Phasor Measurement Units (D-PMUs) [...] Read more.
The rapid growth of Distributed Energy Resources (DERs) has intensified operational challenges in modern distribution networks, especially with respect to observability, bidirectional power flow, feeder model accuracy, and fast event detection. This review critically examines the role of Distribution Phasor Measurement Units (D-PMUs) in this transition. Rather than only listing reported applications, the paper evaluates the technical and practical conditions under which D-PMUs provide meaningful value beyond conventional monitoring technologies. Particular attention is given to state estimation, event detection, ancillary operation, communication latency, synchronization vulnerability, economic viability, and the limited evidence from field deployment. The review shows that D-PMUs are especially attractive at feeder heads, DER interconnection points, switching locations, and microgrid boundaries, where synchronized phase-angle measurements improve visibility of dynamic and unbalanced phenomena. However, widespread deployment is still constrained by cost, communication infrastructure, interoperability, timing security, and the scarcity of publicly documented utility-scale results. The paper concludes by identifying the most promising research directions, including physics-aware learning, graph-based analytics, edge processing, and application-driven placement strategies for DER-rich distribution systems. Full article
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35 pages, 9308 KB  
Article
Tracking Real-Time Anomalies in Cyber–Physical Systems Through Dynamic Behavioral Analysis
by Prashanth Krishnamurthy, Ali Rasteh, Ramesh Karri and Farshad Khorrami
J. Cybersecur. Priv. 2026, 6(2), 55; https://doi.org/10.3390/jcp6020055 - 23 Mar 2026
Viewed by 1467
Abstract
Embedded devices in modern power systems offer increased connectivity and remote reprogrammability/reconfigurability. These features along with interconnections between Information Technology (IT) and Operational Technology (OT) networks enable greater agility, reduced operator workload, and enhanced power system performance and capabilities, as well as expanding [...] Read more.
Embedded devices in modern power systems offer increased connectivity and remote reprogrammability/reconfigurability. These features along with interconnections between Information Technology (IT) and Operational Technology (OT) networks enable greater agility, reduced operator workload, and enhanced power system performance and capabilities, as well as expanding the cyber-attack surface. This increased cyber-attack surface, as well as increasingly complex, diverse, and potentially untrustworthy software/hardware supply chains, increases the need for robust real-time monitoring in power systems, and more generally in cyber–physical systems (CPS). We propose a novel framework for real-time monitoring and anomaly detection in CPS, specifically smart grid substations and SCADA systems. The proposed framework enables real-time signal temporal logic condition-based anomaly monitoring by processing raw captured packets from the communication network through a hierarchical semantic extraction and tag processing pipeline into a time series of semantic events and observations, that are then evaluated against expected temporal properties to detect and localize anomalies. We demonstrate the efficacy of our methodology on a hardware in the loop (HITL) testbed under several attack scenarios. The HITL testbed includes multiple physical power system devices (real-time automation controllers and relays) and simulated devices (Phasor Measurement Units—PMUs, relays, Phasor Data Concentrators—PDCs), all interfaced to a dynamic power system simulator. Full article
(This article belongs to the Section Security Engineering & Applications)
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21 pages, 1511 KB  
Article
SKNet-GAT: A Novel Multi-Source Data Fusion Approach for Distribution Network State Estimation
by Huijia Liu, Chengkai Yin and Sheng Ye
Energies 2026, 19(4), 1012; https://doi.org/10.3390/en19041012 - 14 Feb 2026
Cited by 1 | Viewed by 483
Abstract
This paper tackles the growing uncertainty in distribution networks caused by distributed generation, load fluctuations, and frequent topological changes. It proposes a multi-source data fusion framework using enhanced selective convolution (SKNet) and graph attention networks (GAT). First, heterogeneous measurement data, including Phasor Measurement [...] Read more.
This paper tackles the growing uncertainty in distribution networks caused by distributed generation, load fluctuations, and frequent topological changes. It proposes a multi-source data fusion framework using enhanced selective convolution (SKNet) and graph attention networks (GAT). First, heterogeneous measurement data, including Phasor Measurement Unit (PMU) and Supervisory Control and Data Acquisition (SCADA) data, are processed through a unified normalization and outlier elimination technique to ensure data quality. Second, SKNet is utilized to extract spatiotemporal multi-scale features, improving the detection of both rapid disturbances and long-term trends. Third, the extracted features are fed into GAT to model node electrical couplings, while power flow residual constraints are embedded in the loss function to enforce the physical validity of the estimated states. This physics-informed design overcomes a key limitation of pure data-driven models and enables an end-to-end framework that integrates data-driven learning with physical mechanism constraints. Finally, comprehensive validation is performed on the improved IEEE 33-node and IEEE 123-node test systems. The test scenarios include Gaussian measurement noise, data outliers, missing measurements, and topological changes. The results show that the proposed method outperforms baseline models such as Multi-Scale Graph Attention Network (MS-GAT), Bidirectional Long Short-Term Memory (BiLSTM), and traditional weighted least squares (WLS). It achieves Root Mean Square Error (RMSE) reductions of up to 18% and Mean Absolute Error (MAE) reductions of up to 15%. The average inference latency is only 10–18 ms. Even under unknown topological changes, the estimation error increases by only 15–25%. These results demonstrate the superior accuracy, robustness, and real-time performance of the proposed method for intelligent distribution network state estimation. Full article
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28 pages, 883 KB  
Article
Graph-Guided Genetic Algorithm for Optimal PMU Placement Ensuring Topological and Numerical Observability
by Vladimir Bečejac, Darko Šošić and Aleksandar Savić
Energies 2026, 19(4), 927; https://doi.org/10.3390/en19040927 - 10 Feb 2026
Cited by 1 | Viewed by 523
Abstract
This paper presents a novel hybrid algorithm for determining the optimal Phasor Measurement Units (PMU) configuration in power networks to ensure full topological and numerical observability through a multi-phase process. In the first phase, a graph-theoretic Heuristic Node Selector (HNS) is developed to [...] Read more.
This paper presents a novel hybrid algorithm for determining the optimal Phasor Measurement Units (PMU) configuration in power networks to ensure full topological and numerical observability through a multi-phase process. In the first phase, a graph-theoretic Heuristic Node Selector (HNS) is developed to rapidly establish topological observability via Core-Tree construction and node dominance evaluation. Unlike most existing studies that implicitly assume topological observability implies numerical observability, the second phase applies a Genetic Algorithm to refine and extend the initial solution from HNS, ensuring complete numerical observability while minimizing number of PMUs. This hybrid method significantly reduces the search space and improves convergence. The HNS procedure is further extended in this work to explicitly handle Zero Injection Buses (ZIB) through rule-based topological modifications, enabling a modified version of the algorithm applicable to real networks with complex structures. Real-world implementation practices from European Transmission System Operators are considered through the adoption of a “one PMU per feeder” configuration. The proposed method is validated on standard IEEE test systems and Serbian transmission networks. Results demonstrate high scalability, adaptability to various network topologies (with and without ZIB nodes), and efficient PMU allocation. Notably, the method consistently achieves high values of the System Observability Redundancy Index, indicating strong robustness and redundancy in measurement placement. Full article
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17 pages, 2258 KB  
Article
Modeling and Calibration Using Micro-Phasor Measurement Unit Data for Yeonggwang Substation
by Peng Li, Chung-Gang Kim, Sung-Hyun Choi, Kyung-Min Lee and Yong-Sung Choi
Energies 2026, 19(3), 834; https://doi.org/10.3390/en19030834 - 4 Feb 2026
Viewed by 613
Abstract
Against the backdrop of high-proportion renewable energy grid integration, modeling accuracy for substations incorporating wind and solar power is critical. Traditional modeling methods rely on theoretical parameters and lack sufficient accuracy. This study uses the 154 kV/23 kV Yeonggwang Substation in Jeollanam-do, South [...] Read more.
Against the backdrop of high-proportion renewable energy grid integration, modeling accuracy for substations incorporating wind and solar power is critical. Traditional modeling methods rely on theoretical parameters and lack sufficient accuracy. This study uses the 154 kV/23 kV Yeonggwang Substation in Jeollanam-do, South Korea (connected to three wind farms and three solar power plants, with 35 Micro-Phasor Measurement Unit (μPMU) measurement points deployed) as a case study. It investigates three-phase detailed modeling using Power System Computer Aided Design (PSCAD) and μPMU data-driven calibration. Based on substation topology and equipment parameters, a simulation model encompassing main transformers, transmission lines, renewable energy units, and loads was established. A hierarchical calibration system of “data preprocessing—parameter identification—iterative correction” was constructed, employing an iterative optimization strategy of “main grid layer—renewable energy layer—load layer.” A multi-objective optimization function centered on voltage, current, and power was developed. Verification results show that after calibration, the mean relative error rates (MRE) for voltage, current, active power and reactive power are 2.46%, 2.57%, 2.52% and 3.96% respectively, with mean error reduction rates (MERRs) of 80%, 82.75%, 81.33%, and 74.94% compared to pre-calibration values. The uniqueness of the calibration method proposed in this study lies in its use of actual μPMU measurement data to drive PSCAD model parameter calibration, achieving precise matching with the actual characteristics of the substation. This provides a reference method for modeling and digital twin construction of similar substations, demonstrating significant engineering application value. Full article
(This article belongs to the Special Issue Modeling and Analysis of Power Systems)
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26 pages, 2823 KB  
Article
A Unified Online Assessment Framework for Pre-Fault and Post-Fault Dynamic Security
by Xin Li, Rongkun Shang, Qiao Zhao, Yaowei Zhang, Jingru Liu, Changjie Wu and Panfeng Guo
Energies 2026, 19(3), 673; https://doi.org/10.3390/en19030673 - 27 Jan 2026
Cited by 1 | Viewed by 532
Abstract
With the expansion of interconnection in power systems and the extensive adoption of phasor measurement units (PMUs), the secure operation of power systems has been increasingly covered in research. In this article, a unified online framework for pre-fault and post-fault dynamic security assessment [...] Read more.
With the expansion of interconnection in power systems and the extensive adoption of phasor measurement units (PMUs), the secure operation of power systems has been increasingly covered in research. In this article, a unified online framework for pre-fault and post-fault dynamic security assessment (DSA) is proposed. First, maximum mutual information (MIC) and the random subspace method (RSM) are employed to select the key variables and enhance the diversity of input data, serving as feature engineering. Then, a deep forest (DF) regressor and classifier are utilized respectively to predict security margin (SM) and security state (SS) during online pre-fault and post-fault DSA based on the selected variables. In pre-fault DSA, scenarios with high SM are identified as stable, while those with low SM are forwarded to post-fault DSA. In addition, a time self-adaptive scheme is employed to balance low response time and high prediction accuracy. This approach prevents the misclassification of unstable scenarios as stable by either outputting high-credibility predictions of unstable SS or deferring decisions on SS until the end of the decision-making period. The unified framework, tested on an IEEE 39-bus system and a practical 1648-bus system provided by the PSS/E version 35 software, demonstrates significantly improved assessment accuracy and response times. Specifically, it achieves an average response time (ART) of 2.66 cycles for the IEEE 39-bus system and 3.13 cycles for the 1648-bus system while maintaining an accuracy exceeding 98%, surpassing the performance of currently widely used deep learning models. Full article
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20 pages, 1369 KB  
Article
Symmetry-Aware Interpretable Anomaly Alarm Optimization Method for Power Monitoring Systems Based on Hierarchical Attention Deep Reinforcement Learning
by Zepeng Hou, Qiang Fu, Weixun Li, Yao Wang, Zhengkun Dong, Xianlin Ye, Xiaoyu Chen and Fangyu Zhang
Symmetry 2026, 18(2), 216; https://doi.org/10.3390/sym18020216 - 23 Jan 2026
Viewed by 678
Abstract
With the rapid advancement of smart grids driven by renewable energy integration and the extensive deployment of supervisory control and data acquisition (SCADA) and phasor measurement units (PMUs), addressing the escalating alarm flooding via intelligent analysis of large-scale alarm data is pivotal to [...] Read more.
With the rapid advancement of smart grids driven by renewable energy integration and the extensive deployment of supervisory control and data acquisition (SCADA) and phasor measurement units (PMUs), addressing the escalating alarm flooding via intelligent analysis of large-scale alarm data is pivotal to safeguarding the safe and stable operation of power grids. To tackle these challenges, this study introduces a pioneering alarm optimization framework based on symmetry-driven crowdsourced active learning and interpretable deep reinforcement learning (DRL). Firstly, an anomaly alarm annotation method integrating differentiated crowdsourcing and active learning is proposed to mitigate the inherent asymmetry in data distribution. Secondly, a symmetrically structured DRL-based hierarchical attention deep Q-network is designed with a dual-path encoder to balance the processing of multi-scale alarm features. Finally, a SHAP-driven interpretability framework is established, providing global and local attribution to enhance decision transparency. Experimental results on a real-world power alarm dataset demonstrate that the proposed method achieves a Fleiss’ Kappa of 0.82 in annotation consistency and an F1-Score of 0.95 in detection performance, significantly outperforming state-of-the-art baselines. Additionally, the false positive rate is reduced to 0.04, verifying the framework’s effectiveness in suppressing alarm flooding while maintaining high recall. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Data Analysis)
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23 pages, 9799 KB  
Article
Inertia Estimation of Regional Power Systems Using Band-Pass Filtering of PMU Ambient Data
by Kyeong-Yeong Lee, Sung-Guk Yoon and Jin Kwon Hwang
Energies 2026, 19(2), 424; https://doi.org/10.3390/en19020424 - 15 Jan 2026
Cited by 2 | Viewed by 1435
Abstract
This paper proposes a regional inertia estimation method in power systems using ambient data measured by phasor measurement units (PMUs). The proposed method employs band-pass filtering to suppress the low-frequency influence of mechanical power and to attenuate high-frequency noise and discrepancies between rotor [...] Read more.
This paper proposes a regional inertia estimation method in power systems using ambient data measured by phasor measurement units (PMUs). The proposed method employs band-pass filtering to suppress the low-frequency influence of mechanical power and to attenuate high-frequency noise and discrepancies between rotor speed and electrical frequency. By utilizing a simple first-order AutoRegressive Moving Average with eXogenous input (ARMAX) model, this process allows the inertia constant to be directly identified. This method requires no prior model order selection, rotor speed estimation, or computation of the rate of change of frequency (RoCoF). The proposed method was validated through simulation on three benchmark systems: the Kundur two-area system, the IEEE Australian simplified 14-generator system, and the IEEE 39-bus system. The method achieved area-level inertia estimates within approximately ±5% error across all test cases, exhibiting consistent performance despite variations in disturbance models and system configurations. The estimation also maintained stable performance with short data windows of a few minutes, demonstrating its suitability for near real-time monitoring applications. Full article
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31 pages, 5378 KB  
Article
Composite Fractal Index for Assessing Voltage Resilience in RES-Dominated Smart Distribution Networks
by Plamen Stanchev and Nikolay Hinov
Fractal Fract. 2026, 10(1), 32; https://doi.org/10.3390/fractalfract10010032 - 5 Jan 2026
Cited by 2 | Viewed by 526
Abstract
This work presents a lightweight and interpretable framework for the early warning of voltage stability degradation in distribution networks, based on fractal and spectral features from flow measurements. We propose a Fast Voltage Stability Index (FVSI), which combines four independent indicators: the Detrended [...] Read more.
This work presents a lightweight and interpretable framework for the early warning of voltage stability degradation in distribution networks, based on fractal and spectral features from flow measurements. We propose a Fast Voltage Stability Index (FVSI), which combines four independent indicators: the Detrended Fluctuation Analysis (DFA) exponent α (a proxy for long-term correlation), the width of the multifractal spectrum Δα, the slope of the spectral density β in the low-frequency range, and the c2 curvature of multiscale structure functions. The indicators are calculated in sliding windows on per-node series of voltage in per unit Vpu and reactive power Q, standardized against an adaptive rolling/first-N baseline, and anomalies over time are accumulated using the Exponentially Weighted Moving Average (EWMA) and Cumulative SUM (CUSUM). A full online pipeline is implemented with robust preprocessing, automatic scaling, thresholding, and visualizations at the system level with an overview and heat maps and at the node level and panel graphs. Based on the standard IEEE 13-node scheme, we demonstrate that the Fractal Voltage Stability Index (FVSI_Fr) responds sensitively before reaching limit states by increasing α, widening Δα, a more negative c2, and increasing β, locating the most vulnerable nodes and intervals. The approach is of low computational complexity, robust to noise and gaps, and compatible with real-time Phasor Measurement Unit (PMU)/Supervisory Control and Data Acquisition (SCADA) streams. The results suggest that FVSI_Fr is a useful operational signal for preventive actions (Q-support, load management/Photovoltaic System (PV)). Future work includes the calibration of weights and thresholds based on data and validation based on long field series. Full article
(This article belongs to the Special Issue Fractional-Order Dynamics and Control in Green Energy Systems)
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19 pages, 8178 KB  
Article
SpectralNet-Enabled Root Cause Analysis of Frequency Anomalies in Solar Grids Using μPMU
by Arnabi Modak, Maitreyee Dey, Preeti Patel and Soumya Prakash Rana
Energies 2026, 19(1), 268; https://doi.org/10.3390/en19010268 - 4 Jan 2026
Viewed by 720
Abstract
The rapid integration of solar power into distribution grids has intensified challenges related to frequency instability caused by fluctuating renewable generation. These unexpected frequency variations are difficult to capture using traditional or supervised methods because they emerge from nonlinear, rapidly changing inverter grid [...] Read more.
The rapid integration of solar power into distribution grids has intensified challenges related to frequency instability caused by fluctuating renewable generation. These unexpected frequency variations are difficult to capture using traditional or supervised methods because they emerge from nonlinear, rapidly changing inverter grid interactions and often lack labelled examples. To address this, the present work introduces a unique, frequency-centric framework for unsupervised detection and root cause analysis of grid anomalies using high-resolution micro-Phasor Measurement Unit (μPMU) data. Unlike previous studies that focus primarily on voltage phasors or rely on predefined event labels, this work employs SpectralNet, a deep spectral clustering approach, integrated with autoencoder-based feature learning to model the nonlinear interactions between frequency, ROCOF, voltage, and current. These methods are particularly effective for unexpected frequency variations because they learn intrinsic, hidden structures directly from the data and can group abnormal frequency behavior without prior knowledge of event types. The proposed model autonomously identifies distinct root causes such as unbalanced loads, phase-specific faults, and phase imbalances behind hazardous frequency deviations. Experimental validation on a real solar-integrated distribution feeder in the UK demonstrates that the framework achieves superior cluster compactness and interpretability compared to traditional methods like K-Means, GMM, and Fuzzy C-Means. The findings highlight SpectralNet’s capability to uncover subtle, nonlinear patterns in μPMU data, offering an adaptive, data-driven tool for enhancing grid stability and situational awareness in renewable-rich power systems. Full article
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