Search Results (144)

The development of the global positioning system in conjunction with information and communication technology has resulted in the development of modern power systems, known as smart grids, which automatically permit the monitoring of energy flow as well as the response to any change in the supply or demand of energy. In order to accomplish these goals, the vector of measurements used in conventional state estimation has been expanded to include synchronized phasor measurements provided by accurate measuring devices known as phasor measurement units (PMUs). This study presents practical empirical methods for optimal PMU placement, which seek the minimum number of PMUs to be installed and their corresponding locations. The data pertaining to the power system topology and the interconnections of buses are recorded in appropriate matrices, which are organized according to the number of branches directly connected to each bus and the probability that each bus could serve as candidate for PMU installation. The effectiveness of the proposed methods is verified on different IEEE test systems in the presence or absence of zero injections (ZIs). Full article

The increasing penetration of wind and photovoltaic (PV) generation introduces frequent operating-point variations into transmission networks, while missing supervisory control and data acquisition/phasor measurement unit (SCADA/PMU) measurements and bad data may further weaken the reliability of online state estimation. Conventional weighted least squares (WLS) estimators have a clear physical interpretation, but repeated online matrix solutions may become burdensome in large-scale rolling estimation. To address this issue, this paper proposes a graph–physics-constrained fast state estimation method with bad data detection (BDD) and filtering. Wind/PV-load operating scenarios are constructed on standard test systems, and mixed SCADA/PMU measurements are represented with missing masks and bad data perturbations. The filled measurements, measurement availability mask, and residual anomaly scores are used as input features, while the network topology is converted into a graph Laplacian prior. A regularized fast mapping, graph Laplacian smoothing, and threshold-calibrated residual screening are combined to obtain online state estimates and bad data labels. Five-seed case studies compare the proposed method with WLS and Huber robust WLS. In case300, the average online time is reduced from $66.063\pm 3.054$ ms for WLS to $1.922\pm 0.374$ ms for the proposed method, corresponding to a speedup of about 35.08 times. The results indicate that the proposed linearized prototype is most promising as a fast large-scale rolling estimator or abnormality screener, rather than as a full replacement for model-based estimators in all scenarios. Full article

The wide deployment of phasor measurement units has enabled data-driven transient stability prediction (TSP) of power systems. However, ensuring the reliability of TSP results is still a significant challenge that limits the practical application of data-driven methods. To this end, a convolutional neural network (CNN)-based deep ensemble model with optimized class-specific thresholds is proposed to achieve reliable TSP. Specifically, a CNN is utilized as the backbone predictor, where the time-series variables from multiple generators are transformed into image-like inputs, and a CNN-based deep ensemble model is developed to provide accurate confidence estimation for TSP. Subsequently, considering the asymmetric importance of different classes in TSP, a confidence-based class-specific thresholds rule is adopted, and a multi-objective optimization model for determining the class-specific thresholds is formulated. In this optimization model, the reliability requirement of TSP is imposed as a constraint, requiring that true unstable rate (TUR) equal to 100%, with the objectives of minimizing the rejection rate and maximizing the true stable rate (TSR). The Pareto front of the class-specific thresholds can be obtained by solving the optimization model. Test results on two benchmark power systems show that the proposed method achieves a TUR of 100% and a TSR of at least 99% with approximately 10% of the samples rejected, demonstrating its effectiveness and scalability. Full article

Accurate harmonic estimation at the per-cycle timescale is increasingly required in modern power-quality (PQ) monitoring, where fast-varying distortion sources demand high temporal resolution. However, when harmonic phasors are estimated from a single cycle using windowed discrete Fourier transform techniques, off-nominal fundamental frequency introduces spectral interference between harmonics, leading to systematic amplitude and phase errors that conventional correction methods cannot remove. This paper presents a lightweight, non-iterative harmonic estimation module designed to operate on fixed-rate, one-cycle data streams. The method leverages a frequency estimate provided by an external tracker to explicitly model the spectral interference induced by windowing under off-nominal conditions. By formulating this effect as a linear mixing process, the proposed approach applies an algebraic inversion to recover unbiased harmonic phasors without requiring adaptive resampling, variable window lengths, or modifications to the acquisition system. The module is designed as a plugin component compatible with existing PQ processing chains and shared sampled-value architectures. Experimental validation across frequency sweeps, Monte Carlo noise trials, and dynamic streaming scenarios demonstrates machine-precision accuracy in ideal conditions and noise-limited performance in realistic settings. Compared to iterative alternatives, the proposed solution achieves equivalent accuracy with a $484\times$ reduction in computation time. A sensitivity analysis further quantifies the relationship between frequency-tracking accuracy and harmonic estimation error, providing practical guidelines for system integration. These results show that accurate, real-time harmonic estimation can be achieved from single-cycle data using fixed-rate acquisition, enabling improved monitoring and protection capabilities in modern power systems. Full article

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

Hybrid transmission corridors combining overhead lines and underground cables introduce impedance discontinuities that significantly modify electromagnetic transient behavior. These discontinuities generate traveling-wave reflections, waveform distortions, and high-frequency components at relay measurement locations during the first microseconds following disturbance inception. This paper presents a waveform-level electromagnetic transient (EMT) analysis of overhead–cable transition effects using detailed EMTP-RV simulations including frequency-dependent line and cable models, tower representations, grounding systems, and instrument transformers within a differential protection measurement framework. The results show that overhead–cable transitions produce transient waveform modifications characterized by reflections, attenuation, dispersion, and temporary current imbalance mechanisms associated with traveling-wave propagation and cable capacitive effects. The analysis also demonstrates the transient evolution of instantaneous waveform-derived (EMT-derived) differential and restraining current quantities, defined as combinations of terminal current signals obtained directly from EMT waveforms. These quantities do not represent final phasor-domain operating values of practical numerical relays, but provide insight into the transient electromagnetic environment preceding conventional filtering and phasor estimation. The study contributes to a clearer physical interpretation of transient phenomena in hybrid transmission systems and supports EMT-based evaluation of signals relevant to differential protection applications. Full article

Low-voltage distribution networks are critical for supplying power to end-users, and electric shock safety is a key concern; however, the frequent incompleteness of topology information in practical operations makes it challenging to accurately assess electric shock risks. This paper proposes a two-stage approach for electric shock simulation and risk assessment in low-voltage distribution networks with completely unknown topology and absent phase-angle measurements, addressing the critical challenge of unavailable, incomplete, or outdated topology information using only conventional smart meter data. It innovatively investigates shock risks under TT, TN-C, and TN-S grounding systems without prior topology knowledge or synchronized phasors. The proposed methodology combines a phase-angle-agnostic data-driven stage and a model-driven stage: the data-driven stage uses an iterative algorithm for topology label matrix estimation and weighted Laplacian matrix reconstruction with hierarchical clustering to identify network structure and line parameters, requiring only active power, reactive power, voltage magnitude, and current magnitude. The model-driven stage adopts modified nodal analysis with the finite-difference time-domain (MNA-FDTD) method to evaluate transient leakage voltage distribution under single-phase-to-ground faults, thereby assessing electric shock risks in line with international safety standards. Key contributions include a practical phase-free topology identification framework, comparative risk analysis of three grounding systems, and an integrated data-model approach for real-world low-observability networks. Simulation results show accurate topology/parameter identification with a relative Frobenius-norm error of only 1.8% even without phase data. TN-S provides the highest safety complying with IEC standards, followed by TN-C and TT under specific conditions, offering a practical solution for utilities lacking detailed topology records. Full article

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

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

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

As the complexity of power systems continues to increase and the penetration rate of distributed generation (DG) rises, traditional distance protection schemes face a dual, severe challenge. Specifically, the non-negligible fault transition resistance in grounding faults often leads to underreach, compromising protection speed, while the fault current contribution from integrated DG units severely distorts the measured impedance, increasing the risk of maloperation or failure to trip. To overcome these critical limitations, this study proposes an improved distance protection scheme that simultaneously accounts for and effectively compensates for both fault transition resistance and the impact of DG integration. By leveraging the known $R/X$ ratios of transmission lines and employing voltage–current phasor analysis, the proposed method enables the accurate and rapid estimation/correction of the line impedance between the relay and the fault point. This work provides a robust and low-cost solution for protective decision-making in contemporary power systems. Full article

Lyapunov-exponent-based diagnostics are widely used to quantify deterministic chaos in optically injected semiconductor lasers (OISLs). In most numerical implementations, the optical field is represented either in phasor coordinates $(A,\psi ,N)$ or in Cartesian quadrature coordinates $(X,Y,N)$. Although these representations are mathematically related through a smooth coordinate transformation away from vanishing field amplitude, their numerical realizations can exhibit markedly different robustness in variational calculations, directly impacting the reliability of Lyapunov exponent estimation and chaoticity maps. In this work, we present a systematic assessment of the numerical reliability of Lyapunov-based chaos analysis in master-slave optically injected semiconductor lasers using both phasor and quadrature formulations. The full Lyapunov spectrum was computed via a noise-free variational method that integrates the nonlinear dynamics together with the corresponding Jacobian equations using a fourth-order Runge-Kutta scheme combined with periodic QR orthonormalization. High-resolution Lyapunov maps were constructed in the injection strength-frequency detuning parameter space, and the consistency between both formulations was quantitatively evaluated. While both approaches reproduce the overall structure of chaotic and non-chaotic regions, the phasor formulation may generate spurious positive Lyapunov exponents in regimes where the optical field amplitude approaches low values. These discrepancies originate from singular terms proportional to $1/A$ and $1/A^2$ in the variational Jacobian of the phasor model, which can lead to numerical amplification and artificial chaotic signatures. The quadrature formulation avoids these singularities and provides numerically stable and physically consistent Lyapunov spectra across the explored parameter space. The results establish practical guidelines for robust chaos quantification in optically injected semiconductor lasers and highlight the importance of representation choice in variational Lyapunov analysis of nonlinear photonic systems. Full article

This study presents adaptive virtual inertia strategy supported by a model-predictive-control (MPC)-based real-time inertia estimation method. The proposed approach aims to mitigate frequency stability problems caused by low inertia in isolated power systems with high penetration of photovoltaics. The system inertia is estimated using frequency measurements obtained from phasor measurement unit. Based on the obtained real-time inertia information, the PI gains ($K_p$ and $K_i$) in load frequency control unit and virtual inertia gain ($K_{vi}$) are updated simultaneously via MPC-based adaptive mechanism. In the first scenario, it was shown that under 10% PV penetration, the system inertia decreased from 5.00 s to 4.54 s, and the system became more sensitive to load changes. The proposed adaptive battery energy storage system support shows that a load change of 0.1 p.u. results in a response of 0.079 p.u. in 0.17 s. The adaptive BESS response raises frequency nadir from 49.6892 Hz to 49.9635 Hz, improving maximum frequency deviation by 88.25%. In the second scenario, it was observed that method maintained its stability even when the system inertia dropped to 3.33 s in 10–50% PV penetration range. This study presents integrated and innovative frequency control strategy for modern isolated power systems. Full article

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

Modern protection relays require accurate and fast phasor estimation under harsh transient conditions, including a decaying DC component, harmonics, interharmonics, noise, and frequency instability. The original CCHDF (Cleaned Characteristic Harmonic Digital Filter) produced a harmonic cleaned signal using the Biunivocal Frequency Relationship of Phasors (BFRP) technique, but relied on DFT, Hanning windowing, and peak detection to identify interharmonic components. This paper replaces that spectral estimation block with the Modified Covariance Method (MCM) estimator, a high resolution autoregressive (AR) spectral estimator capable of superior frequency, magnitude, and phase estimation of non-harmonic components even with a short data window. The result is an improved filter named MCCCHDF (Modified Covariance CCHDF), preserving the original algorithmic pipeline, but achieving higher accuracy and faster convergence in the presence of closely spaced harmonics/interharmonics and noisy decaying DC conditions. Full article