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High‐breakdown‐point estimators of multivariate location and shape matrices, such as the MM‐estimator with smoothed hard rejection and the Rocke S‐estimator, are generally designed to have high efficiency for Gaussian data. However, many phenomena are non‐Gaussian, and these estimators can therefore have poor efficiency. This article proposes a new tunable S‐estimator, termed the Sq‐estimator, for the general class of symmetric elliptical distributions, a class containing many common families such as the multivariate Gaussian, t‐, Cauchy, Laplace, hyperbolic, and normal inverse Gaussian distributions. Across this class, the Sq‐estimator is shown to generally provide higher maximum efficiency than other leading high‐breakdown estimators while maintaining the maximum breakdown point. Furthermore, the Sq‐estimator is demonstrated to be distributionally robust, and its robustness to outliers is demonstrated to be on par with these leading estimators while also being more stable with respect to initial conditions. From a practical viewpoint, these properties make the Sq‐estimator broadly applicable for practitioners. These advantages are demonstrated with an example application—the minimum‐variance optimal allocation of financial portfolio investments. [ABSTRACT FROM AUTHOR]

A modern power system is characterized by an increasing penetration of wind power, which results in large uncertainties in its states. These uncertainties must be quantified properly; otherwise, the system security may be threatened. Facing this challenge, we propose a cost-effective, data-driven approach to assessing a power system's load margin probabilistically. Using actual wind data, a kernel density estimator is applied to infer the nonparametric wind speed distributions, which are further merged into the framework of a vine copula. The latter enables us to simulate complex multivariate and highly dependent model inputs with a variety of bivariate copulae that precisely represent the tail dependence in the correlated samples. Furthermore, to reduce the prohibitive computational time of traditional Monte-Carlo simulations that process a large amount of samples, we propose to use a nonparametric, Gaussian-process-emulator-based reduced-order model to replace the original complicated continuation power-flow model through a Bayesian-learning framework. To accelerate the convergence rate of this Bayesian algorithm, a truncated polynomial chaos surrogate, which serves as a highly efficient, parametric Bayesian prior, is developed. This emulator allows us to execute the time-consuming continuation power-flow solver at the sampled values with a negligible computational cost. Results of simulations that are performed on several test systems reveal the impressive performance of the proposed method in the probabilistic load-margin assessment. [ABSTRACT FROM AUTHOR]

• Robust Complex-Valued Levenberg-Marquardt algorithm. • Bi-quadratic convergence property. • Rectangular coordinates and quadratic mismatch functions. • Easier computer implementation. This paper deals with a robust complex-valued Levenberg-Marquardt algorithm specially developed for solving ill-conditioned power flow problems. Moreover, it can also be a useful tool for voltage instability and voltage collapse studies. Because power flow models are nonlinear, the Wirtinger calculus is applied to develop iterative algorithms based on Taylor series expansions of nonlinear functions of complex variables and their complex conjugates. Our proposal in complex plane is straightforward derived in rectangular coordinates. Consequently, its performance is compared to the well-known optimized multiplier based load flow method. Aiming this purpose, we show that few changes in the codes are required to transform the complex-valued Newton-Raphson power flow algorithm into the complex-valued Levenberg-Marquardt power flow one. Furthermore, we show that the latter lends itself well to modeling new smart grid technologies while exhibiting a bi-quadratic convergence rate and superior performance as compared to the former procedure. The performance of our proposal is demonstrated and analyzed on well-conditioned IEEE-14, −30, −57 and −118 bus systems and the Brazilian Southern-equivalent system termed SIN-1916 bus. Furthermore, its performance is also demonstrated on the ill-conditioned IEEE-11, −43 bus systems besides the SIN-1916 under stressed operating conditions or higher R / X ratios of transmission lines. [ABSTRACT FROM AUTHOR]

Due to physical or control-related limitations, some dynamic state variables are constrained, such as the regulated voltage, the exciter reference voltage, etc. In addition, there exists a set of algebraic constraints that exactly confines the evolution of the system states. However, a systematic way to fully consider all inequality and equality constraints is lacking in the existing dynamic state estimation (DSE) literature. This paper proposes a general constrained robust DSE framework that is able to deal with various equality and inequality constraints. The project operator is integrated with the pseudo-measurements formulation in a unique manner to address the inequality and equality constraints, respectively, within the unscented Kalman filter (UKF) framework, which relies on the unscented transformation and is derivative-free. To this end, the derivative-free robust UKF is extended to address all the constraints while maintaining its robustness to measurement noise and bad data. Numerical results on the IEEE 39-bus system show that the proposed method exhibits the following benefits: first, improved accuracy of the state estimates in the presence of measurement noise; second, enhanced convergence speed and ability to address weakly observed dynamic state variables; and third, enhanced capability to deal with bad data and cyber attacks. [ABSTRACT FROM AUTHOR]

The generalized polynomial chaos (gPC) method recently advocated in the literature, exhibits impressive efficiency and accuracy in probabilistic power flow (PPF) calculations of small-scale power systems. However, it suffers from the “curse of dimensionality” and can only be applied to systems with input random variables that follow a set of standard probability distributions. This paper overcome these weaknesses by developing a hierarchical polynomial chaos analysis of variance (ANOVA) method that shows excellent performances in terms of accuracy, efficiency, rationality, and adaptability, for small- to large-scale power systems. By proving the equivalence between the polynomial chaos expansion and the ANOVA decomposition, which is executed at no extra computational cost, the dimensionality of the polynomial chaos expansion can be adaptively reduced to improve the computational efficiency of the generalized polynomial chaos method in high-dimensional problems. Furthermore, by resorting to the Stieltjes procedure, it is extended to any assumed probability distributions of the input random variables. Simulation results carried out on the IEEE 118-bus system and the 1354-bus European high voltage system with correlated renewable energy generations reveal that the developed method outperforms the generalized polynomial chaos method and the Monte Carlo (MC) method while being compatible with real-time applications in power systems. [ABSTRACT FROM AUTHOR]

This paper presents a new theoretical framework that, by integrating robust statistics and robust control theory, allows us to develop a robust dynamic state estimator of a cyber-physical system. This state estimator combines the generalized maximum-likelihood-type (GM) estimator, the unscented Kalman filter (UKF), and the H-infinity filter into a robust H-infinity UKF filter in the Krein space, which is able to handle large system uncertainties as well as suppress outliers while achieving a good statistical efficiency under Gaussian and non-Gaussian process and observation noises. Specifically, we first use the statistical linearization approach to build a linearlike regression model in the Krein space. Then, we show that the H-infinity UKF is just the Krein space Kalman filter that exhibits a bounded estimation error in presence of system uncertainties while minimizing the least squares criterion; consequently, it suffers from a lack of robustness to outliers and non-Gaussian noise. Because the GM estimator is able to handle outliers, but it may yield large estimation errors in the presence of system uncertainties, we propose to combine it with the H-infinity UKF in a robust H-infinity UKF. We carry out a theoretical analysis to demonstrate the connections that our filter has with the H-infinity UKF and the GM-UKF. The good performance of the new filter is demonstrated via extensive simulation performed on the IEEE 39-bus power system. [ABSTRACT FROM AUTHOR]

Quantifying the uncertainty of the renewable energy generation units and loads is critical to ensure the dynamic security of next-generation power systems. To achieve that goal, the time-consuming Monte Carlo simulations are usually used, which is not suitable for online dynamic analysis of large-scale power systems. To circumvent this difficulty, two uncertainty quantification approaches using polynomial-chaos-based methods are proposed and investigated. The first approach is the generalized polynomial chaos method that is able to reduce the computing time by three orders of magnitude compared with Monte Carlo methods while achieving the same accuracy. We find that this approach is very useful for short-term power system dynamic simulations, but it may produce unreliable results for long-term simulations. To address the weakness of that approach, we present the second method, namely the multi-element generalized-polynomial-chaos method. It is seen that this method is more accurate and more numerically stable than the generalized polynomial chaos method. Since the uncertainties of the renewable energy generation units and loads can follow very different distributions, we extend the Stieltjes’ recursive procedure that allows us to derive the orthogonal basis functions for any assumed probability distribution of the input random variables. Extensive simulations carried out on the WECC 3-machine 9-bus system and the New England 10-machine 39-bus system reveal that our proposed approaches are able to produce comparable accuracy as the Monte Carlo based method while achieving significantly improved computational efficiency for both stable and unstable power system operating conditions. [ABSTRACT FROM AUTHOR]

Real-time state information provided by the state estimator plays a major role in power system monitoring and control. As a result, the convergence of the estimator under various system operating conditions becomes one of the key requirements. In this paper, a state estimation framework that achieves both statistical and numerical robustness is proposed. This estimation framework also generalizes several well-known estimators, including the weighted least squares estimator, the least absolute value estimator, the Huber Maximum-likelihood-estimator, and the Schweppe-type Huber generalized Maximum-likelihood (SHGM)-estimator. The statistical robustness of each estimator has been studied analytically through the total influence function. In addition, the dependence between the statistical robustness of an estimator and the numerical robustness of the iterative algorithm is investigated. To enhance the numerical robustness of the iterative algorithm that solves the SHGM-estimator, a fourth-order Levenberg–Marquardt approach-based SHGM (LM-SHGM) estimator is proposed. It integrates the statistical robustness of that estimator to address various types of bad data and the numerical robustness of the LM approach to handle highly stressed operating conditions. Numerical results carried out on the IEEE test systems demonstrate the good convergence and robustness of the proposed approach under various operating conditions. [ABSTRACT FROM AUTHOR]

This paper develops a robust generalized maximum-likelihood Koopman operator-based Kalman filter (GM-KKF) to estimate the rotor angle and speed of synchronous generators. The approach is data driven and model independent. Its design phase is carried out offline and requires estimates of the synchronous generators’ rotor angle and speed, along with active and reactive power at the generators’ terminal; in real-time operation, only measurements of the rotor speed, active, and reactive power are used. We first investigate the probability distribution of the transformed dynamic states by means of Q–Q plots and verify that the states of the GM-KKF approximately follow a Student's t-distribution with 20 degrees of freedom when the initial state vector is normally distributed. Under this assumption, our filter presents high statistical efficiency. Numerical simulations carried out on the IEEE 39-bus test system reveal that the GM-KKF has a faster convergence rate than the non-robust Koopman operator-based Kalman filter thanks to the adoption of a batch-mode regression formulation. They also show that the computing time of the GM-KKF is roughly reduced by one-third as compared to the one taken by our previously developed robust GM-extended Kalman filter. [ABSTRACT FROM AUTHOR]

This paper develops a generalized framework that allows us to investigate the vulnerability of the power system nonlinear state estimator to false data injection attacks (FDIAs) from the operator's perspective and to initiate some countermeasures. Unlike most existing FDIA methods, which assume a perfect knowledge of the system measurements and topology by a hacker, we derive and analyze the uncertainties for launching successful FDIAs along with their upper bounds. To effectively defend against an FDIA, we propose a robust detector that checks the measurement statistical consistency using a subset of secure PMU measurements. We first show that if these secure PMU measurements are free of bad data while making the system observable, the FDIA is detectable. We then show that detectability is also ensured if these conditions are relaxed while using alternative redundant measurements from short-term nodal synchrophasor predictions together with the robust Huber M-estimator. Numerical simulation results on the IEEE 30-bus and 118-bus systems demonstrate the effectiveness and robustness of the proposed method even the secure measurements contain noise and bad data. [ABSTRACT FROM AUTHOR]

The largest normalized residual statistical test (LNRT) is claimed to have the ability to detect noncritical single or multiple interacting but nonconforming bad data. However, we show in this letter that this claim does not always hold true for bad leverage points. Specifically, we prove that while a single noncritical and nonleverage measurement that is corrupted by a sufficiently large gross error is likely to be detected, the same measurement in a position of leverage and corrupted by the same gross error is unlikely to be detected. Furthermore, we show that multiple noncritical bad leverage points that are topologically adjacent to each other naturally form one or several groups of interacting bad data, which may cause the LNRT to fail. Since leverage points are common in actual power systems, the LNRT is doomed to frequently fail to detect bad data. Simulation results carried out on IEEE 30-bus system validate our theoretical results. [ABSTRACT FROM AUTHOR]

Accurate local bus frequency is essential for power system frequency regulation provided by distributed energy sources, flexible loads, and among others. This paper proposes a robust frequency divider (RFD) for online bus frequency estimation. Our RFD is independent of the load models, and the knowledge of swing equation parameters, transmission line parameters, and local Phasor Measurement Unit (PMU) measurements at each generator terminal bus is sufficient. In addition, it is able to handle several types of data quality issues, such as measurement noise, gross measurement errors, cyberattacks, and measurement losses. Furthermore, the proposed RFD contains the decentralized estimation of local generator rotor speeds and the centralized bus frequency estimation, which resembles the structure of the decentralized/hierarchical control scheme. This enables RFD for very large-scale system applications. Specifically, we decouple each generator from the rest of the system by treating metered real power injection as inputs and the frequency measurements provided by PMU as outputs; then a robust unscented Kalman filter based dynamic state estimator is proposed for local generator rotor speed estimation; finally, these rotor speeds are transmitted to control center for bus frequency estimation. Numerical results carried out on the IEEE 39-bus and 145-bus systems demonstrate the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a fast and robust unscented Kalman filter based decentralized dynamic state estimator (DSE) for power system online monitoring and control. The proposed robust DSE is able to detect, identify, and suppress three types of outliers, namely the observation, innovation, and structural outliers. Observation outliers refer to the received PMU measurements providing unreliable metered values due to gross errors or cyber attacks; innovation outliers are typically caused by impulsive system process noise, whereas structural outliers are induced by incorrect parameters of the generators or its associated controllers, such as exciters and speed governors. To enable the fast estimation of generator states of large-scale power systems in a decentralized manner, two model decoupling approaches are presented and compared. It is shown that the generator decoupling approach presented in this paper achieves higher statistical efficiency than the ones proposed in the literature in the presence of both small and large measurement noise. To detect and distinguish three types of outliers, projection statistics based multiple hypothesis testing approach is proposed. Specifically, three hypotheses corresponding to the occurrence of three types of outliers are assumed by constructing three innovation matrices; these matrices are made up by time-correlated innovation vectors, and/or predicted states, and/or measurements; then projection statistics are applied to each of the innovation matrix and its calculated projection values are checked by a statistical test to validate the assumed hypothesis. The identified outliers are further suppressed by a generalized maximum-likelihood-type estimator. Numerical results carried out on the IEEE 39-bus system demonstrate the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper develops a robust estimator of correlation as a data preprocessing stage to the Prony method that is able to suppress white impulsive noise. The method consists of the following steps. First, the bus voltage magnitudes and phase angles are combined to build a set of complex-valued measurements. Second, the outliers of the complex-valued data samples, which are induced by impulsive noise, are identified and suppressed using the iteratively reweighted phase–phase correlator; the latter is a robust estimator of correlation for complex-valued Gaussian processes, which has been extended here to handle outliers in both magnitude and phase angle of voltage phasor measurements. Finally, the classical Prony method is applied on the robustly estimated voltage phase angles. The good performance of the proposed method is demonstrated through simulations carried out on the two-area four-machine system, on the simplified WECC 179-bus system, as well as on real PMU data. Simulation results show that the method is very fast to compute and is compatible with real-time application requirements. [ABSTRACT FROM AUTHOR]

Since their inceptions, the multimodal imaging techniques have received a great deal of attention for achieving enhanced imaging performance. In this work, a novel joint reconstruction framework using sparse computed tomography (CT) and magnetic resonance imaging (MRI) data is developed and evaluated. CT and MRI images are synchronously acquired and registered from a hybrid CT-MRI platform. Because image data are highly undersampled, analytic methods are unable to generate decent image quality. To overcome this drawback, we resort to the compressed sensing (CS) techniques, which employ sparse priors that result from an application of a wavelet transform. To utilize multimodal information, projection distance is introduced and is tuned to tailor the texture and pattern of the final images. Specifically, CT and MRI images are alternately reconstructed using the updated multimodal results that are calculated at the latest step of the iterative optimization algorithm. The method exploits the structural similarities shared by the CT and MRI images to achieve better reconstruction quality. The good performance of the proposed approach is demonstrated on a pair of undersampled CT and MRI body images. Clinical CT and MRI images are tested with the joint reconstruction, the analytic reconstruction, and the independent reconstruction which does not uses multimodal imaging information. Results show that the proposed method improves about 5dB in signal to noise ratio (SNR) and nearly 10% in structural similarity measure comparing to independent reconstruction. It offers similar quality with fully sampled analytic reconstruction with only 20% sampling rate for CT and 40% for MRI. Structural similarities and correlations residing in images from different modalities are useful to mutually promote the quality of image reconstruction. [ABSTRACT FROM AUTHOR]

Several hierarchical centralized control schemes for either rotor angle or voltage stability improvement have been proposed in the literature. They all rely on exchanging information between different subsystems of a large-scale power system. By contrast, in this paper, we propose a hierarchical decentralized control scheme to enhance a unified manner rotor angle and voltage stability while using metered values collected within each subsystem, without any exchange of information between subsystems. Specifically, weakly coupled coherent areas of a power system are first determined. Then, secondary control agents are implemented in each of them to detect and damp rotor angle and voltage instabilities using local synchrophasor measurements. Decentralized control laws based on Lyapunov theory are implemented on FACTS devices for achieving global rotor angle asymptotic stability. Finally, a tertiary voltage control agent provides reference settings to the secondary voltage agents and takes control actions in case the latter fail to damp voltage instabilities. We show that the proposed scheme minimizes the communication bandwidth requirement while exhibiting a system-wide situational awareness. Simulations carried out on the IEEE 118-bus system demonstrate the effectiveness of the proposed hierarchical decentralized control method. [ABSTRACT FROM PUBLISHER]

This paper proposes a new robust method for accurately and reliably estimating remote bus frequencies in a power system. Two different measurement sources for the remote bus frequency are considered, that is, the ideal Frequency Divider (FD) and the Synchronous Reference Frame Phase Locked Loops (SRF‐PLLs). Each measurement signal encounters different uncertainties and data quality issues. In this paper, both data sources are employed and fused together to better estimate the remote bus frequencies. To this end, the model structure of the power system is selected and an Unscented Kalman Filter (UKF) is utilized together with a fusion covariance intersection method to enhance the accuracy of the estimated bus frequency. Since the fusion estimation method fails in case of quality issues on both channels, a robust Generalized Maximum‐likelihood UKF (GM‐UKF) using a novel outlier detection criteria is developed. The impact of the resulting robust fusion filter on the estimation of the remote bus frequencies and on the performance of WAPSS, which makes use of the estimated frequencies as the feedback signal, is examined via simulations. The results demonstrate the excellent performance and reliability of the proposed method in dealing with noise filtering and outlier suppression while ensuring a high statistical efficiency. [ABSTRACT FROM AUTHOR]

This letter shows that the sparse state recovery optimization method is equivalent to the well-known Huber M-estimator, and then justifies its robustness to bad data. We derive the total influence functions of the Huber M-estimator and the generalized maximum-likelihood (GM)-estimator, and give a formal proof that the Huber M-estimator is vulnerable to bad leverage points while the GM-estimator can handle them. Numerical results carried out on various IEEE systems validate our theoretical results. [ABSTRACT FROM PUBLISHER]

• Guest editorial board. • Special issue. • Data-analytics for stability analysis, control and situational awareness. • Power systems with high penetration of renewable energy. This is the Guest Editorial of the Special Issue on Data-Analytics for Stability Analysis, Control, and Situational Awareness of Power System with High-Penetration of Renewable Energy. [ABSTRACT FROM AUTHOR]

The autocorrelation function is a commonly used tool in statistical time series analysis. In this paper we examine the robustness of two estimators of correlation based on memoryless nonlinear functions of the observations, the Median-of-Ratios Estimator (MRE) and the Phase-Phase Correlator (PPC), which are applicable to complex-valued Gaussian random processes. We show that they are robust to impulsive noise from a bias perspective at the expense of statistical efficiency at the Gaussian distribution. Additionally, we develop iterative versions of these estimators named the IMRE and IPPC, realizing an improved bias performance over their non-iterative counterparts and the well-known robust Schweppe-type Generalized M-estimator utilizing a Huber cost function (SHGM). We use robust Mahalanobis distances generated by the IMRE and IPPC to improve the performance of impulsive noise suppression through the use of weighted basis pursuit methods. These estimation and data-cleaning techniques are applied to both synthetic and actual collected data using an Ettus Research USRP to perform robust spectral estimation on signals from the digital television band in the presence of additive impulsive noise. Finally, the analysis reveals that if the time series is highly correlated and the contamination rate is low, the MRE outperforms the PPC estimator from a variance and bias perspective. However, the PPC is the estimator of choice when the correlation is lower and is better suited to time critical applications due to lower computation costs. [ABSTRACT FROM PUBLISHER]

This paper presents an equally constrained robust estimator of both the state and the transformer tap positions of a power system able to withstand all types of outliers, including bad leverage points and erroneous zero-injections. The statistical robustness of the estimator stems from the application of the Schweppe-type Huber GM estimator (SHGM) while its numerical robustness originates from the use of an orthogonal iteratively re-weighted least-squares algorithm together with the Van Loan's method for processing the equality constraints. The good performance of the new estimator, termed EC-SHGM estimator for short, is demonstrated on a small test system and on the Brazilian Southern power system with increasing size ranging from 139 buses to 1916 buses. It is shown that it exhibits superior convergence properties in all tested cases while the WLS method may suffer from numerical instabilities or even divergence problems when large weights are assigned to zero power injections modeling false information. [ABSTRACT FROM PUBLISHER]

Large-scale blackouts typically result from cascading failure in power systems operation. Their mitigation in power system planning calls for the development of methods and algorithms that assess the risk of cascading failure due to relay overtripping, short-circuits induced by overgrown vegetation, voltage sags, line and transformer overloading, transient instabilities, voltage collapse, to cite a few. This paper describes such a method based on composite power system reliability evaluation via sequential Monte Carlo simulation. One of the impediments of the study of these phenomena is the prohibitively large computational burden involved by the simulations. To overcome this difficulty, importance sampling technique utilizing the Weibull distribution is applied to power generator outages. Another method combing importance sampling and antithetic variates together is implemented as well. It is shown that both methods noticeably reduce the number of samples that need to be investigated while maintaining the accuracy at a given level. It is found that the combined method outperforms importance sampling to certain extent. To illustrate the developed techniques, two case studies are conducted and analyzed on the IEEE one-area and three-area reliability test system. [ABSTRACT FROM PUBLISHER]

Using only the phase information and a relationship based on the Gaussian Hypergeometric function, the Phase-Phase Correlator can be utilized to estimate the normalized cross-correlation coefficient between two zero-mean complex Gaussian processes. This estimator naturally introduces a certain robustness to white impulsive observation noise over the Gaussian Maximum Likelihood estimator. This correspondence examines the robustness of the Phase-Phase Correlator in the presence of uncorrelated impulsive noise. We show that its asymptotic bias compares favorably to the robust Schweppe-type GM-estimator with the Huber function termed SHGM at a cost of efficiency. Application of the PPC to autoregressive time series analysis is illustrated with a parametric spectral estimation example. [ABSTRACT FROM PUBLISHER]

A new robust Kalman filter is proposed that detects and bounds the influence of outliers in a discrete linear system, including those generated by thick-tailed noise distributions such as impulsive noise. Besides outliers induced in the process and observation noises, we consider in this paper a new type called structural outliers. For a filter to be able to counter the effect of these outliers, observation redundancy in the system is necessary.We have therefore developed a robust filter in a batch-mode regression form to process the observations and predictions together, making it very effective in suppressing multiple outliers. A key step in this filter is a new prewhitening method that incorporates a robust multivariate estimator of location and covariance. The other main step is the use of a generalized maximum likelihood-type (GM) estimator based on Schweppe's proposal and the Huber function, which has a high statistical efficiency at the Gaussian distribution and a positive breakdown point in regression. The latter is defined as the largest fraction of contamination for which the estimator yields a finite maximum bias under contamination. This GM-estimator enables our filter to bound the influence of residual and position, where the former measures the effects of observation and innovation outliers and the latter assesses that of structural outliers. The estimator is solved via the iteratively reweighted least squares (IRLS) algorithm, in which the residuals are standardized utilizing robust weights and scale estimates. Finally, the state estimation error covariance matrix of the proposed GM-Kalman filter is derived from its influence function. Simulation results revealed that our filter compares favorably with the H∞-filter in the presence of outliers. [ABSTRACT FROM AUTHOR]

The ability to detect defects on hardwood trees and logs holds great promise for the hardwood forest products industry. At every stage of wood processing, there is a potential for improving value and recovery with knowledge of the location, size, shape, and type of log defects. This paper deals with a new method that processes hardwood laser-scanned surface data for defect detection. The detection method is based on robust circle fitting applied to scanned cross-section data sets recorded along the log length. It can be observed that these data sets have missing data and include large outliers induced by loose bark that dangles from the log trunk. Because of that and because of the nonlinearity of the circle model, which presents both additive and nonadditive errors, we initiated a new robust Generalized M-estimator for which the residuals are standardized via scale estimates calculated by means of projection statistics and incorporated in the Huber objective function, yielding a bounded influence method. Our projection statistics are based on the 2-D radial vectors instead of the row vectors of the Jacobian matrix as advocated in the literature dealing with linear regression. These radial distances allow us to develop algorithms aimed at pin. pointing large surface rises and depressions from the contour image levels, and thereby, locating severe external defects having at least a height of 0.5 in and a diameter of 5 in. [ABSTRACT FROM AUTHOR]

The real-time estimation of the AC power system equivalent parameters enables the grid-connected Voltage Source Converter (VSC) to achieve more effective stability control during a short-circuit fault. In this paper, a novel Thevenin Equivalent (TE) parameter estimation method based on local synchronous Phasor Measurement Units (PMUs) is proposed and applied to the Phase-Locked Loop (PLL) synchronization stability control of VSC. First, the relationship between the variation of the measured voltage and the error of the estimated impedance is strictly derived based on the rules of norm inequality. Then, according to the analysis of the upper bound of the system voltage change, a voltage threshold is proposed to select the PMU measurements to ensure the accuracy of the estimation during the large disturbance. Finally, using the estimated TE parameters, the current control instruction of VSC during the fault is calculated in real-time to ensure a synchronous and stable operation. The simulations reveal that the proposed estimation method can accurately track the TE parameters after a fault. Furthermore, the associated current control actions during a fault can ensure the PLL synchronization stability of VSC. [ABSTRACT FROM AUTHOR]

We propose a Koopman operator-based surrogate model for propagating parameter uncertainties in power system nonlinear dynamic simulations. First, we augment a priori known state-space model by reformulating parameters deemed uncertain as pseudo-state variables. Then, we apply the Koopman operator theory to the resulting state-space model and obtain a linear dynamical system model. This transformation allows us to analyze the evolution of the system dynamics through its Koopman eigenfunctions, eigenvalues, and modes. Of particular importance for this letter, the obtained linear dynamical system is a surrogate that enables the evaluation of parameter uncertainties by simply perturbing the initial conditions of the Koopman eigenfunctions associated with the pseudo-state variables. Simulations carried out on the New England test system reveal the excellent performance of the proposed method in terms of accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

The sun is constantly emitting electrons and ions as a magnetized plasma, forming the solar wind and carrying with it the sun's rotating magnetic field. The solar wind subsequently interacts with Earth's magnetosphere and the magnetospheres of other planets. Occasionally large amounts of magnetized plasma is released at one time in a Corona mass ejection (CME). When the CME interacts with Earth's magnetic field, it induces perturbations that may have a significant impact on critical infrastructure, for instance, by disturbing communication systems, and inducing currents on pipelines and electric power lines, which in turn may cause increased corrosion or blackouts, among other effects. In this paper, we analyze measured electrical signals provided to us by the Finnish Meteorological Institute, which were induced by geomagnetic storms on pipelines located in Finland and recorded in 2003. Specifically, we perform a wavelet leader multifractal analysis of these current signals to generate singularity spectra, and then using the bootstrapping technique we apply statistical tests to show that these signals exhibit multifractal characteristics. • The GIC data showed multifractal behavior over the data analyzed. • As the K p index increases, the first cumulant shows a trend towards increasing magnitude, with significant variance • Source of the multifractal behavior most likely comes from the complex interactions of the sun with Earth's magnetosphere. • Wavelet leader method along with the bootstrap method enabled statistical hypothesis testing for multifractal behavior. • Surrogate data testing helped provided additional statistical hypothesis testing for multifractal behavior. [ABSTRACT FROM AUTHOR]

Serving as a prerequisite to power system dynamic state estimation, the observability analysis of a power system dynamic model has recently attracted the attention of many power engineers. However, because this model is typically nonlinear and large-scale, the analysis of its observability is a challenge to the traditional derivative-based methods. Indeed, the linear-approximation-based approach may provide unreliable results while the nonlinear-technique-based approach inevitably faces extremely complicated derivations. Furthermore, because power systems are intrinsically stochastic, the traditional deterministic approaches may lead to inaccurate observability analyses. Facing these challenges, we propose a novel polynomial-chaos-based derivative-free observability analysis approach that not only is free of any linear approximations, but also accounts for the stochasticity of the dynamic model while bringing a low implementation complexity. Furthermore, this approach enables us to quantify the degree of observability of a stochastic model, what conventional deterministic methods cannot do. The excellent performance of the proposed method has been demonstrated by performing extensive simulations using a synchronous generator model with IEEE-DC1A exciter and the TGOV1 turbine governor. [ABSTRACT FROM AUTHOR]

In this letter, a novel Gaussian process emulator is proposed, for the first time, to conduct the probabilistic power-flow calculation. Based on Bayesian inference, a Gaussian process emulator is trained and served as a nonparametric, reduced-order model of the nonlinear power-flow model. This emulator allows us to evaluate the time-consuming power-flow solver at the sampled values with a negligible computational cost. The simulations reveal the excellent performance of this method. [ABSTRACT FROM AUTHOR]

This paper develops a robust power system state estimation framework that accounts for correlations and imperfect time synchronization of the measurements. In this framework, correlations of the measurements obtained from the supervisory control and data acquisition (SCADA) system and the phasor measurement units (PMUs) are separately calculated through the unscented transformation and a vector auto-regression (VAR) model. Specifically, the PMU measurements during the waiting period of two successive SCADA measurement scans are buffered via a VAR model whose parameters are robustly estimated using the projection statistics. The latter take into account their temporal and spatial correlations and provide the needed measurement redundancy to suppress bad data and mitigate imperfect time synchronization. In the case where the SCADA and the PMU measurements do not arrive simultaneously at the control center, yielding imperfect measurement time synchronization, either the forecasted PMU measurements or the prior SCADA measurements from the latest state estimation run are leveraged to restore system observability. Finally, a robust generalized maximum-likelihood (GM)-estimator is extended to integrate the measurement error correlations and to handle the outliers, also known as bad data. Simulation results that stem from a comprehensive comparison with other alternatives under various conditions demonstrate the benefits of the proposed framework. [ABSTRACT FROM AUTHOR]

This paper develops a robust iterated extended Kalman filter (EKF) based on the generalized maximum likelihood approach (termed GM-IEKF) for estimating power system state dynamics when subjected to disturbances. The proposed GM-IEKF dynamic state estimator is able to track system transients in a faster and more reliable way than the conventional EKF and the unscented Kalman filter (UKF) thanks to its batch-mode regression form and its robustness to innovation and observation outliers, even in position of leverage. Innovation outliers may be caused by impulsive noise in the dynamic state model while observation outliers may be due to large biases, cyber attacks, or temporary loss of communication links of PMUs. Good robustness and high statistical efficiency under Gaussian noise are achieved via the minimization of the Huber convex cost function of the standardized residuals. The latter is weighted via a function of robust distances of the two-time sequence of the predicted state and innovation vectors and calculated by means of the projection statistics. The state estimation error covariance matrix is derived using the total influence function, resulting in a robust state prediction in the next time step. Simulation results carried out on the IEEE 39-bus test system demonstrate the good performance of the GM-IEKF under Gaussian and non-Gaussian process and observation noise. [ABSTRACT FROM AUTHOR]

The U.S. Naval Research Laboratory is developing a rep-rate charger for a 60-kJ capacitor module. The charger is lithium-ion battery powered and must charge up the capacitive load 50 times over a 5-min period with roughly 1 s between each charge cycle. This paper examines some aspects of the design: lithium-ion battery energy storage, hard switched dc–dc converter, high-voltage rectifier, and capacitive load with pulsed power switching. The lithium-ion batteries are arranged in 12, 16-cell, 50 V modules that are connected in series to form a roughly 600 V prime power supply. A hard switched dc–dc converter with full-bridge rectifier is used to charge the capacitor and a pulse forming network is used to discharge the capacitor into the load. This paper will discuss the system design and available test data. [ABSTRACT FROM PUBLISHER]

The reliable operation of a power distribution system relies on a good prior knowledge of its topology and its system state. Although crucial, due to the lack of direct monitoring devices on the switch statuses, the topology information is often unavailable or outdated for the distribution system operators for real-time applications. Apart from the limited observability of the power distribution system, other challenges are the nonlinearity of the model, the complicated, unbalanced structure of the distribution system, and the scale of the system. To overcome the above challenges, this paper proposes a Bayesian-inference framework that allows us to simultaneously estimate the topology and the state of a three-phase, unbalanced power distribution system. Specifically, by using the very limited number of measurements available that are associated with the forecast load data, we efficiently recover the full Bayesian posterior distributions of the system topology under both normal and outage operation conditions. This is performed through an adaptive importance sampling procedure that greatly alleviates the computational burden of the traditional Monte-Carlo (MC)-sampling-based approach while maintaining a good estimation accuracy. The simulations conducted on the IEEE 123-bus test system and an unbalanced 1282-bus system reveal the excellent performances of the proposed method. [ABSTRACT FROM AUTHOR]

• We'd like to emphasize that the algorithm presented in the paper is an enhancement of the Iwamoto's approach [2] once the correction applied to the state variables happens at each iteration instead of just once. In this latter case, probably it was motivated by the processor accuracy informed in [2] which was in that time 5.0 × 10−4 (IBM 370/135). • On the other hand, in the enhanced power flow solution the Jacobian matrix is factorized at each iteration through a very efficient QR algorithm which is a square root- and division-free Givens rotations [12]. • Additionally, we have extended the proposed algorithm to deal with ill-conditioned networks. Thus, the robustness of the Levenberg-Marquardt algorithms as presented in [8] is preserved, but its computational efficiency is substantially increased once the number of iterations to achieve the solution is reduced in average to half. In this paper an enhanced power flow algorithm in complex plane is proposed. The power flow models in complex plane is naturally developed in Cartesian coordinates, thus most of the constraints equations can be written as quadratic functions. Consequently, the Taylor series expansion stops in the third term and the exact nonlinearity of the quadratic complex power flow equations is retained while the remaining functions are dealt through the Newton-Raphson method. Minor changes in the codes are required to transform the Newton-Raphson method into the enhanced power flow approach in complex plane. The new algorithm exihibits either a superior behavior in well- or ill-conditioned networks. The features and advantages of the proposed algorithm are illustrated through a small example and case studies carried out either on the well- or ill-conditioned fashion of the IEEE-14, −30, −57 and −118 bus and the Brazilian Southern-equivalent of 1916-buses, termed as SIN-1916. [ABSTRACT FROM AUTHOR]

Sensing and measurement systems are quintessential to the safe and reliable operation of electric power grids. Their strategic placement is of ultimate importance because it is not economically viable to install measurement systems on every node and branch of a power grid, though they need to be monitored. An overwhelming number of strategies have been developed to meet oftentimes multiple conflicting objectives. The prime challenge in formulating the problem lies in developing a heuristic or an optimisation model that, though mathematically tractable and constrained in cost, leads to trustworthy technical solutions. Further, large‐scale, long‐term deployments pose additional challenges because the boundary conditions change as technologies evolve. For instance, the advent of new technologies in sensing and measurement, as well as in communications and networking, might impact the cost and performance of available solutions and shift initially set conditions. Also, the placement strategies developed for transmission grids might not be suitable for distribution grids, and vice versa, because of unique characteristics; therefore, the strategies need to be flexible, to a certain extent, because no two power grids are alike. Despite the extensive literature on the present topic, the focus of published works tends to be on a specific subject, such as the optimal placement of measurements to ensure observability in transmission grids. There is a dearth of work providing a comprehensive picture for developing optimal placement strategies. Because of the ongoing efforts on the modernisation of electric power grids, there is a need to consolidate the status quo while exposing its limitations to inform policymakers, industry stakeholders, and researchers on the research‐and‐development needs to push the boundaries for innovation. Accordingly, this paper first reviews the state‐of‐the‐art considering both transmission and distribution grids. Then, it consolidates the key factors to be considered in the problem formulation. Finally, it provides a set of perspectives on the measurement placement problem, and it concludes with future research directions. [ABSTRACT FROM AUTHOR]

Dynamic state estimation (DSE) accurately tracks the dynamics of a power system and provides the evolution of the system state in real-time. This paper focuses on the control and protection applications of DSE, comprehensively presenting different facets of control and protection challenges arising in modern power systems. It is demonstrated how these challenges are effectively addressed with DSE-enabled solutions. As precursors to these solutions, reformulation of DSE considering both synchrophasor and sampled value measurements and comprehensive comparisons of DSE and observers have been presented. The usefulness and necessity of DSE based solutions in ensuring system stability, reliable protection and security, and resilience by revamping of control and protection methods are shown through examples, practical applications, and suggestions for further development. [ABSTRACT FROM AUTHOR]

In this paper, the stochastic characteristics of the electric consumption in France are analyzed. It is shown that the load time series exhibit lasting abrupt changes in the stochastic pattern, termed breaks. The goal is to propose an efficient and robust load forecasting method for prediction up to a day-ahead. To this end, two new robust procedures for outlier identification and suppression are developed. They are termed the multivariate ratio-of-medians-based estimator (RME) and the multivariate minimum-Hellinger-distance-based estimator (MHDE). The performance of the proposed methods has been evaluated on the French electric load time series in terms of execution times, ability to detect and suppress outliers, and forecasting accuracy. Their performances are compared with those of the robust methods proposed in the literature to estimate the parameters of SARIMA models and of the multiplicative double seasonal exponential smoothing. A new robust version of the latter is proposed as well. It is found that the RME approach outperforms all the other methods for “normal days” and presents several interesting properties such as good robustness, fast execution, simplicity, and easy online implementation. Finally, to deal with heteroscedasticity, we propose a simple novel multivariate modeling that improves the quality of the forecast. [ABSTRACT FROM PUBLISHER]

Proposes a supervisory level power system stabilizer using wide area measurements. Importance of power system stabilizers to system oscillations; Descriptions of the controller design process; Application of agent technology to power systems; Discussion on the multiagent damping control structure and the corresponding communication techniques.

Power system dynamic state estimation (DSE) remains an active research area. This is driven by the absence of accurate models, the increasing availability of fast-sampled, time-synchronized measurements, and the advances in the capability, scalability, and affordability of computing and communications. This paper discusses the advantages of DSE as compared to static state estimation, and the implementation differences between the two, including the measurement configuration, modeling framework and support software features. The important roles of DSE are discussed from modeling, monitoring and operation aspects for today's synchronous machine dominated systems and the future power electronics-interfaced generation systems. Several examples are presented to demonstrate the benefits of DSE on enhancing the operational robustness and resilience of 21st century power system through time critical applications. Future research directions are identified and discussed, paving the way for developing the next generation of energy management systems and novel system monitoring, control and protection tools to achieve better reliability and resiliency. [ABSTRACT FROM AUTHOR]

Accurate estimates of the electromechanical disturbance propagation in a power system play an important role in taking preventive, corrective, and in-extremis control actions. This paper proposes an analytical method for disturbance propagation investigation based on the electromechanical wave theory. A frame structure model is developed that allows us to derive an analytical relationship between the disturbance propagation and the turbine-generator inertia, the line reactance, bus voltage, and disturbance source frequency. In addition, the disturbance attenuation and the degree of disturbance propagation are studied. Numerical results performed on a multi-machine chain network and the IEEE 118-bus test system demonstrate the effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

The maximum active power that a Line-Commutated-Converter High Voltage Direct Current (LCC-HVDC) can provide instantly, called LCC-HVDC-MC Maximum Emergency Power Capacity, is an important information for determining the emergency control strategy of a power system subject to a large disturbance. However, it is a challenging task to calculate this capacity accurately due to system model uncertainties and contingencies. To address this problem, we propose to estimate this capacity by real-time tracking the Thevenin equivalent (TE) parameters of the AC system based on local PMUs. This new TE estimation method can handle the large disturbances and yield an accurate HVDC-MC while considering various constraints. Specifically, we first investigate the impacts of the TE potential changes on the TE impedance estimation under a large disturbance. To reduce the estimation error caused by the TE potential change, we develop an adaptive current screening process of the current measurements. Moreover, we use the total least square estimation method to further filter out the PMU errors. Finally, we calculate LCC-HVDC maximum emergency power capacity while accounting for the limitations of the control performance, voltage dependent current order limit, the converter capacity, and the AC voltage. The simulations show that the proposed method can accurately track the TE parameters and the real-time LCC-HVDC maximum emergency power capacity following a large disturbance. [ABSTRACT FROM AUTHOR]

This paper proposes a new methodology for power system islanding based on Koopman modal coherency (KMC) combined with subgraph theory. Initial system partitioning is determined from the Koopman bus-angle coherency matrix. Then, the technique of subgraph is used to modulate the partitions, yielding to viable islands. Balancing subgraphs are constructed from the clusters pairwise neighboring areas. Overload subgraphs swap to connected over-generation subgraphs. Stable islands satisfy nonlinear dynamic coherency, and minimal power mismatch. The search algorithm substantiates the required bands specified in the frequency operating standards. Under severe disturbances, over-frequency generation shedding and under-frequency load shedding schemes are implemented. The proposed islanding methodology is demonstrated on a realistic 151-bus, 24-machines power system. Results show that the proposed scheme can reduce failure regions in faulted power systems. [ABSTRACT FROM AUTHOR]

This paper summarizes the technical activities of the Task Force on Power System Dynamic State and Parameter Estimation. This Task Force was established by the IEEE Working Group on State Estimation Algorithms to investigate the added benefits of dynamic state and parameter estimation for the enhancement of the reliability, security, and resilience of electric power systems. The motivations and engineering values of dynamic state estimation (DSE) are discussed in detail. Then, a set of potential applications that will rely on DSE is presented and discussed. Furthermore, a unified framework is proposed to clarify the important concepts related to DSE, forecasting-aided state estimation, tracking state estimation, and static state estimation. An overview of the current progress in DSE and dynamic parameter estimation is provided. The paper also provides future research needs and directions for the power engineering community. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editors discuss reports within the issue, including "Nonlinear Electrical Circuit Oscillator Control Based on Backstepping Method: A Genetic Algorithm Approach," "Function Projective Synchronization of a Class of Chaotic Systems With Uncertain Parameters," and "Lag Synchronization of Coupled Multidelay Systems."

Modern society relies heavily upon complex and widespread electric grids. In recent years, advanced sensors, intelligent automation, communication networks, and information technologies (IT) have been integrated into the electric grid to enhance its performance and efficiency. Integrating these new technologies has resulted in more interconnections and interdependencies between the physical and cyber components of the grid. Natural disasters and man-made perturbations have begun to threaten grid integrity more often. Urban infrastructure networks are highly reliant on the electric grid and consequently, the vulnerability of infrastructure networks to electric grid outages is becoming a major global concern. In order to minimize the economic, social, and political impacts of large-scale power system outages, the grid must be resilient in addition of being robust and reliable. The concept of a power system’s cyber-physical resilience centers around maintaining critical functionality of the system backbone in the presence of unexpected extreme disturbances. Resilience is a multidimensional property of the electric grid; it requires managing disturbances originating from physical component failures, cyber component malfunctions, and human attacks. In the electric grid community, there is not a clear and universally accepted definition of cyber-physical resilience. This paper focuses on the definition of resilience for the electric grid and reviews key concepts related to system resilience. This paper aims to advance the field not only by adding cyber-physical resilience concepts to power systems vocabulary, but also by proposing a new way of thinking about grid operation with unexpected extreme disturbances and hazards and leveraging distributed energy resources. The concepts of service availability and quality are not new, but many recognize the need of resilience in maintaining essential services to critical loads, for example to allow home refrigerators to operate for food conservation in the aftermath of a hurricane landfall. By providing a comprehensive definition of power system resilience, this paper paves the way for creating appropriate and effective resilience standards and metrics. [ABSTRACT FROM AUTHOR]

This paper describes the upper level of a two-tiered sustainability assessment framework (SAF) for determining the optimal synthesis/design and operation of a power network and its associated energy production and storage technologies. The upper-level framework is described, and results for its application to a test bed scenario given by the Northwest European electricity power network presented. A brief description of the lower level of the SAF is given as well. In order to analyze the impact of microgrids (MGs) in the main network, two different scenarios are considered in the analysis, i.e., a network without MGs and a network with MGs. The optimization is carried out in a multi-objective, quasi-stationary manner with producer partial-load behavior taken into account via nonlinear functions for efficiency, cost, and emissions that depend on the electricity generated by each nonrenewable or renewable producer technology. Results indicate for the particular problem posed and for the optima! configurations found that including MGs improves the network relative to reductions in capital and operating costs and to increases in network resiliency. On the other hand, total daily SO2 emissions and network exergetic efficiency are not improved for the case when MGs are included. [ABSTRACT FROM AUTHOR]

Abstract: We develop a framework to assess and quantify the sustainability and reliability of different power production scenarios in a regional system, focusing on the interaction of microgrids with the existing transmission/distribution grid. The Northwestern European electricity market (Belgium, France, Germany and the Netherlands) provides a case study for our purposes. We present simulations of power market outcomes under various policies and levels of microgrid penetration, and evaluate them using a diverse set of metrics. This analysis is the first attempt to include exergy-based and reliability indices when evaluating the role of microgrids in regional power systems. The results suggest that a power network in which fossil-fueled microgrids and a price on CO2 emissions are included has the highest composite sustainability index. [Copyright &y& Elsevier]