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This paper presents a dynamic event data-based stability risk assessment method for power grids with high penetrations of inverter-based resources (IBRs). This method relies on obtaining the IBRs’ DQ admittance through dynamic event data and computing the system’s eigenvalues based on the admittance models. Two critical technologies are employed in this research, including time-domain and frequency-domain data fitting and $dq$ -frame voltage and current signal derivation. The first technology is key to obtaining the $s$ -domain expressions from the transient response data, and the $s$ -domain DQ admittance model from the frequency-domain measurements. The second technology is key to obtaining the $dq$ -frame voltage and current signals from either the three-phase instantaneous measurements or the phasor measurement unit (PMU) data. The method is illustrated using data generated from a Type-4 wind power plant modeled in PSCAD. This paper demonstrates the technical feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

Let $\mathrm {W}\in \mathbb {C}^{n\times n}$ be a single-spiked Wishart matrix in the class $\mathrm {W}\sim \mathcal {CW}_{n}(m,\mathrm {I}_{n}+ \theta \mathrm {v}\mathrm {v}^{\dagger}) $ with $m\geq n$ , where ${\mathrm {I}}_{n}$ is the $n\times n$ identity matrix, $\mathrm {v}\in \mathbb {C}^{n\times 1}$ is an arbitrary vector with unit Euclidean norm, $\theta \geq 0$ is a non-random parameter, and $(\cdot)^{\dagger} $ represents the conjugate-transpose operator. Let u1 and ${\mathrm {u}}_{n}$ denote the eigenvectors corresponding to the smallest and the largest eigenvalues of W, respectively. This paper investigates the probability density function (p.d.f.) of the random quantity $Z_{\ell }^{(n)}=\left |{\mathrm {v}^{\dagger} \mathrm {u}_\ell }\right |^{2}\in (0,1)$ for $\ell =1,n$. In particular, we derive a finite dimensional closed-form p.d.f. for $Z_{1}^{(n)}$ which is amenable to asymptotic analysis as $m,n$ diverges with $m-n$ fixed. It turns out that, in this asymptotic regime, the scaled random variable $nZ_{1}^{(n)}$ converges in distribution to $\chi ^{2}_{2}/2(1+\theta)$ , where $\chi _{2}^{2}$ denotes a chi-squared random variable with two degrees of freedom. This reveals that u1 can be used to infer information about the spike. On the other hand, the finite dimensional p.d.f. of $Z_{n}^{(n)}$ is expressed as a double integral in which the integrand contains a determinant of a square matrix of dimension $(n-2)$. Although a simple solution to this double integral seems intractable, for special configurations of $n=2,3$ , and 4, we obtain closed-form expressions. [ABSTRACT FROM AUTHOR]

In this paper, we propose the $K$ K -Shot Contrastive Learning (KSCL) of visual features by applying multiple augmentations to investigate the sample variations within individual instances. It aims to combine the advantages of inter-instance discrimination by learning discriminative features to distinguish between different instances, as well as intra-instance variations by matching queries against the variants of augmented samples over instances. Particularly, for each instance, it constructs an instance subspace to model the configuration of how the significant factors of variations in $K$ K -shot augmentations can be combined to form the variants of augmentations. Given a query, the most relevant variant of instances is then retrieved by projecting the query onto their subspaces to predict the positive instance class. This generalizes the existing contrastive learning that can be viewed as a special one-shot case. An eigenvalue decomposition is performed to configure instance subspaces, and the embedding network can be trained end-to-end through the differentiable subspace configuration. Experiment results demonstrate the proposed $K$ K -shot contrastive learning achieves superior performances to the state-of-the-art unsupervised methods. [ABSTRACT FROM AUTHOR]

Deep learning based models have excelled in many computer vision tasks and appear to surpass humans’ performance. However, these models require an avalanche of expensive human labeled training data and many iterations to train their large number of parameters. This severely limits their scalability to the real-world long-tail distributed categories, some of which are with a large number of instances, but with only a few manually annotated. Learning from such extremely limited labeled examples is known as Few-Shot Learning (FSL). Different to prior arts that leverage meta-learning or data augmentation strategies to alleviate this extremely data-scarce problem, this paper presents a statistical approach, dubbed Instance Credibility Inference (ICI) to exploit the support of unlabeled instances for few-shot visual recognition. Typically, we repurpose the self-taught learning paradigm to predict pseudo-labels of unlabeled instances with an initial classifier trained from the few shot and then select the most confident ones to augment the training set to re-train the classifier. This is achieved by constructing a (Generalized) Linear Model (LM/GLM) with incidental parameters to model the mapping from (un-)labeled features to their (pseudo-)labels, in which the sparsity of the incidental parameters indicates the credibility of the corresponding pseudo-labeled instance. We rank the credibility of pseudo-labeled instances along the regularization path of their corresponding incidental parameters, and the most trustworthy pseudo-labeled examples are preserved as the augmented labeled instances. This process is repeated until all the unlabeled samples are included in the expanded training set. Theoretically, under the conditions of restricted eigenvalue, irrepresentability, and large error, our approach is guaranteed to collect all the correctly-predicted pseudo-labeled instances from the noisy pseudo-labeled set. Extensive experiments under two few-shot settings show the effectiveness of our approach on four widely used few-shot visual recognition benchmark datasets including miniImageNet, tieredImageNet, CIFAR-FS, and CUB. Code and models are released at https://github.com/Yikai-Wang/ICI-FSL. [ABSTRACT FROM AUTHOR]

Let $\mathbf {X}\in \mathbb {C}^{n\times m}$ ($m\geq n$) be a random matrix with independent columns each distributed as complex multivariate Gaussian with zero mean and single-spiked covariance matrix $\mathbf {I}_{n}+ \eta \mathbf {u}\mathbf {u}^{*}$ , where $\mathbf {I}_{n}$ is the $n\times n$ identity matrix, $\mathbf {u}\in \mathbb {C}^{n\times 1}$ is an arbitrary vector with unit Euclidean norm, $\eta \geq 0$ is a non-random parameter, and $(\cdot)^{*}$ represents the conjugate-transpose. This paper investigates the distribution of the random quantity $\kappa _{\text {SC}}^{2}(\mathbf {X})=\sum _{k=1}^{n} \lambda _{k}/\lambda _{1}$ , where $0\le \lambda _{1}\le \lambda _{2}\le \ldots \leq \lambda _{n} < \infty $ are the ordered eigenvalues of $\mathbf {X}\mathbf {X}^{*}$ (i.e., single-spiked Wishart matrix). This random quantity is intimately related to the so called scaled condition number or the Demmel condition number (i.e., $\kappa _{\text {SC}}(\mathbf {X})$) and the minimum eigenvalue of the fixed trace Wishart-Laguerre ensemble (i.e., $\kappa _{\text {SC}}^{-2}(\mathbf {X})$). In particular, we use an orthogonal polynomial approach to derive an exact expression for the probability density function of $\kappa _{\text {SC}}^{2}(\mathbf {X})$ which is amenable to asymptotic analysis as matrix dimensions grow large. Our asymptotic results reveal that, as $m,n\to \infty $ such that $m-n$ is fixed and when $\eta $ scales on the order of $1/n$ , $\kappa _{\text {SC}}^{2}(\mathbf {X})$ scales on the order of $n^{3}$. In this respect we establish simple closed-form expressions for the limiting distributions. It turns out that, as $m,n\to \infty $ such that $n/m\to c\in (0,1)$ , properly centered $\kappa _{\text {SC}}^{2}(\mathbf {X})$ fluctuates on the scale $m^{\frac {1}{3}}$. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the anti-jamming problem of a directional modulation (DM) system with the aid of intelligent reflecting surface (IRS). As an efficient tool to combat malicious jamming, receive beamforming (RBF) is usually designed by using the statistical properties of the jamming received by Bob. Thus, it is very necessary to estimate the receive jamming covariance matrix (JCM) at Bob. To achieve a precise JCM estimation, three JCM estimation methods, including eigenvalue decomposition (EVD), parametric estimation method by gradient descend (PEM-GD) and parametric estimation method by alternating optimization (PEM-AO), are proposed. Here, the proposed EVD is derived according to the rank-2 constraint of JCM. The PEM-GD method fully explores the structure features of JCM and the PEM-AO is proposed to decrease the computational complexity of the former via dimensionality reduction. The simulation results show that the proposed three methods perform better than directly using sample covariance matrix. Additionally, the proposed PEM-GD and PEM-AO outperform EVD method and the clutter and disturbance covariance estimator RCML. [ABSTRACT FROM AUTHOR]

The identification of generator coherency is crucial to design intentional controlled power system islanding. Due to high penetration of nonsynchronous generation, power system inertia changes both temporally and spatially. Thus, the dynamics in system oscillations and associated slow coherency of generators are directly affected by this. Therefore, their sensitivity deserves investigation. In this paper, the slow coherency with variable inertia is systematically discussed by incremental analysis. Specifically, the approach to study the impacts of variable inertia, based on the matrix perturbation theory, is deployed to provide the explicit eigen-solution sensitivity of slow coherency. To investigate the dependency of coherency grouping on inertia, the changing trends of eigenvector and possible alteration of coherency grouping are estimated. The unusual and abrupt alteration of slow coherency is observed in special scenarios near to modal resonance, i.e. close eigenvalue. The analysis in such scenarios was hardly found in the previous work of coherency sensitivity. Since close eigenvalue can make the traditional matrix perturbation inapplicable, the feasible perturbation in such special scenarios is proposed in this paper. The proposed approach has been thoroughly tested using the classic IEEE 118-bus system. The quantitative results are compared with those obtained analytically. [ABSTRACT FROM AUTHOR]

In secure spatial modulation with a malicious full-duplex attacker, how to obtain the interference subspace or channel state information (CSI) is very important for Bob to reduce or even completely cancel the interference from Mallory. In this paper, different from existing work with perfect CSI, the covariance matrix of malicious interference (CMMI) from Mallory is estimated to construct the interference subspace. To improve the estimation accuracy, a CMMI rank detector relying on the Akaike information criterion (AIC) is derived first. To achieve a high-precision CMMI estimation, two methods, principal component analysis-eigenvalue decomposition (PCA-EVD) and joint diagonalization (JD) are proposed. The proposed PCA-EVD is a rank deduction method whereas the JD method is a joint optimization method with improved performance in the low jamming-to-noise ratio (JNR) region at the expense of increased complexity. Simulation results show that the proposed PCA-EVD performs much better than existing methods like sample estimated covariance matrix (SCM) and EVD in terms of normalized mean square error (NMSE) and secrecy rate (SR). Additionally, the proposed JD has achieved a better NMSE performance than PCA-EVD in the low JNR region (JNR $\leq$ 0 dB) while the proposed PCA-EVD performs better than JD in the high JNR region. [ABSTRACT FROM AUTHOR]

This paper proposes an impedance/admittance-based methodology for stability assessment of converter-based device connections to power systems. The proposed methodology is designed to model the dynamics of detailed black-box converter models, derived from impedance frequency response measurements. From the converter’s impedance frequency response measurements, a linear time-invariant (LTI) representation of its dynamics is obtained in the $dq$ domain using a vector fitting technique. This representation is incorporated in the state-space representation of the whole power system in the $dq$ domain, which is used to perform stability assessment considering traditional eigenvalue analysis and participation factors computation. The proposed methodology is tested in the 39 Bus New England system, including detailed models of a VSC windfarm and a modular multilevel converter (MMC) technology-based STATCOM. It has been found that the proposed impedance-based methodology is able to accurately predict the dynamic performance of black-box converter models, unstable operating conditions and converter control interactions between devices. [ABSTRACT FROM AUTHOR]

The problem of maximizing secrecy rate of multiple-input multiple-output multiple-eavesdropper (MIMOME) channels with arbitrary numbers of antennas at each node is studied in this paper. First, the optimization problem corresponding to the secrecy capacity of the MIMOME channel is converted to an equivalent optimization based on Givens rotations and eigenvalue decomposition of the covariance matrix. In this new formulation, precoder is a rotation matrix which results in a positive semi-definite (PSD) covariance matrix by construction. This removes the PSD matrix constraint and makes the problem easier to tackle. Next, a Broyden-Fletcher-Goldfarb-Shanno (BFGS)-based algorithm is developed to find the rotation and power allocation parameters. Further, the generalized singular value decomposition (GSVD)-based precoding is used to initialize this algorithm. The proposed rotation-BFGS method provides an efficient approach to find a near-optimal transmit strategy for the MIMOME channel and outperforms various state-of-the-art analytical and numerical methods. In particular, the rotation-BFGS precoding achieves higher secrecy rates than the celebrated GSVD precoding, with a reasonably higher computational complexity. Extensive numerical results elaborate on the effectiveness of the rotation-BFGS precoding. The new framework developed in this paper can be applied to a variety of similar problems in the context of multi-antenna channels with and without secrecy. [ABSTRACT FROM AUTHOR]

Construction of the linearized state-space model is the key step of eigenvalue analysis for SSO study of power systems with large-scale renewable power generation (RPG) integrated. This paper proposes a novel method to construct the state matrix of the AC/DC hybrid power system with RPG within the discrete-time domain. The continuous-time state-space model of each AC/DC component as well as RPG units in the power system, is discretized together with their corresponding control. The discretized equation of each component is then represented by an equivalent circuit consisting of parallel historical current and conductance. According to the power system configuration, the discrete-time equivalent circuit of the whole AC/DC hybrid system is established, and the nodal analysis method is applied for the construction of the discrete-time state-space model of the power system. In this way, the state matrix can be acquired much more conveniently than that of continuous-time state-space method, which needs topology analysis to find independent state variables of the network from the proper tree. The proposed method has been applied in the eigenvalue analysis for the SSO study of a case system adapted from the AC/DC hybrid transmission system in northwest China. Eigenvalue results are in high accordance with time-domain simulation results in PSCAD/EMTDC. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel transmission scheme, called sparse layered MIMO (SL-MIMO), that combines non-orthogonal transmission and singular value decomposition (SVD) precoding. Non-orthogonality in SL-MIMO allows re-using of the eigen-channels which improves the spectral efficiency and error rate performance of the system through enhancing the coding gain and diversity gain. We also present a low-complexity message-passing (MP) detector for the proposed SL-MIMO system which performs quite close to maximum likelihood (ML). The joint moment generating function (MGF) of the ordered eigenvalues is calculated and used to derive a closed-form upper bound on the average word error probability (AWEP) of the SL-MIMO system, and this derived expression is then used to analyze the diversity gain of the system. We use our analytical results to design sub-optimal codebooks to minimize the error rate of the SL-MIMO system. Simulation results in $4\times 4$ and $6\times 6$ multiple-input multiple-output (MIMO) systems with 4-ary, 16-ary, and 64-ary constellations show that our proposed SL-MIMO scheme outperforms competing approaches such as X- and Y-codes in terms of system error rate performance. SL-MIMO has 5.6 dB advantage compared to X-codes and 4.7 dB advantage compared to Y-codes in $6\times 6$ MIMO system with a 64-ary constellation. [ABSTRACT FROM AUTHOR]

Heterogeneous information network (HIN) embedding aims at learning the low-dimensional representation of nodes while preserving structure and semantics in a HIN. Existing methods mainly focus on static networks, while a real HIN usually evolves over time with the addition (deletion) of multiple types of nodes and edges. Because even a tiny change can influence the whole structure and semantics, the conventional HIN embedding methods need to be retrained to get the updated embeddings, which is time-consuming and unrealistic. In this paper, we investigate the problem of dynamic HIN embedding and propose a novel Dynamic HIN Embedding model (DyHNE) with meta-path based proximity. Specifically, we introduce the meta-path based first- and second-order proximities to preserve structure and semantics in HINs. As the HIN evolves over time, we naturally capture changes with the perturbation of meta-path augmented adjacency matrices. Thereafter, we learn the node embeddings by solving generalized eigenvalue problem effectively and employ eigenvalue perturbation to derive the updated embeddings efficiently without retraining. Experiments show that DyHNE outperforms the state-of-the-arts in terms of effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

In this paper, detectability analysis is studied and extended to guide selection of measurements for the dynamic state estimation (DSE) of a synchronous machine. To make sure that the DSE converges, past studies suggested that enough measurements must be available to make the system observable. In this paper, the convergence condition is relaxed via detectability analysis to reduce the number of required measurements. Because the objective of the DSE is to estimate the current states as time progresses, it is shown that a DSE observer can converge not only for an observable system but also for an unobservable system if the eigenvalues corresponding to the unobservable states are stable. Simulation results using the IEEE 10-machine, 39-bus system show that the unscented-Kalman-filter-based DSE can converge when measurements are chosen such that the unobservable states have stable eigenvalues. In comparison with observability analysis, the proposed application of detectability analysis can reduce the number of measurements required for the existence of a DSE observer. [ABSTRACT FROM AUTHOR]

Blind noise-level estimation (NLE) is a fundamental issue in digital image processing. This paper provides a noise-level estimator for additive white Gaussian noise and multiplicative Gaussian noise using principal texture patches (PTPs). The proposed algorithm first identifies the principal texture of the noisy image by using the principal component analysis, and then, it chooses PTPs to calculate the noise level. The major contributions of this paper toward addressing the challenges in the NLE literature include: 1) analyzing the nonlinear relationship between the smallest eigenvalue, true noise level, number of chosen patches, and block size; 2) extracting PTPs; and 3) computing noise level using PTPs. The abundant experimental results show that the proposed method works well for various natural images over a large range of noise levels and it performs well for multiplicative noise. Compared with some state-of-the-art approaches, our method has the best performance and a faster running speed. [ABSTRACT FROM AUTHOR]

This paper develops a grey-box approach to small-signal stability analysis of complex power systems that facilitates root-cause tracing without requiring disclosure of the full details of the internal control structure of apparatus connected to the system. The grey-box enables participation analysis in impedance models, which is popular in power electronics and increasingly accepted in power systems for stability analysis. The Impedance participation factor is proposed and defined in terms of the residue of the whole-system admittance matrix. It is proved that, the so defined impedance participation factor equals the sensitivity of the whole-system eigenvalue with respect to apparatus impedance. The classic state participation factor is related to the impedance participation factor via a chain-rule. Based on the chain-rule, a three-layer grey-box approach, with three degrees of transparency, is proposed for root-cause tracing to different depths, i.e. apparatus, states, and parameters, according to the available information. The association of impedance participation factor with eigenvalue sensitivity points to the re-tuning that would stabilize the system. The impedance participation factor can be measured in the field or calculated from the black-box impedance spectra with little prior knowledge required. [ABSTRACT FROM AUTHOR]

This paper proposes an inequality constraints based method to efficiently and quickly estimate stability regions of droop control slopes for modular multilevel converter (MMC)-based multi-terminal dc (MTDC) systems. At first, a general small-signal model of the MMC-MTDC system is developed, which consists of the dc network and the MMCs with $dq$ controllers and multiple droop controllers. When deriving corresponding nonlinear state-space models, the edge-node matrix is introduced for the dc network modeling with arbitrary grid topology and transmission line model. Then, based on the eigenvalues sensitivity and the Taylor Series of eigenvalues, a set of inequality constraints are proposed to expeditiously estimate the suprema of the droop slopes and identify the droop slope stability regions for the MMC-MTDC system. To verify the state-space model, a comparison of dynamic responses between the math model calculation in MATLAB and the EMT simulation in PSCAD/EMTDC is conducted, which demonstrates the accuracy and the correctness of the developed small-signal model. The effectiveness of the proposed parameter stability region estimation method is demonstrated by several examinations including the supremum tests of droop slopes, the stability region sketches on accuracy, and the predicted unstable operations in PSCAD/EMTDC. [ABSTRACT FROM AUTHOR]

This paper proposes an improved stochastic estimation method based on contour integral to estimate the number of critical eigenvalues. The stochastic estimation method transforms the eigenvalue numbers' calculation into summing the traces of a series of inverse matrices. And then, a stochastic strategy is used to estimate the trace of the inverse matrix. However, the method results in an unacceptable error when the state matrices of many practical power systems are ill-conditioned. To solve this problem, the improved algorithm is proposed by formulating a satisfactory matrix for trace calculation artificially instead of randomly with the help of the well-known greedy algorithm based on graph coloring. It is proved to be much more reliable when dealing with ill matrix. The proposed method based on contour integral is very suitable for large-scale power systems due to the element distribution of descriptor matrices makes it possible to construct only one fixed matrix at all integral points. Moreover, the calculation efficiency is further improved by calculating implicitly without destroying the sparsity of descriptor systems. Numerical experiments indicate that the proposed method can significantly improve accuracy without considerably increasing the calculation time. And the approximate eigenvalue number can fully meet the needs of subsequent algorithms based on contour integral to calculate the specific eigenvalues. [ABSTRACT FROM AUTHOR]

Agnostic matrix phase retrieval (AMPR) is a general low-rank matrix recovery problem given a set of noisy high-dimensional data samples. To be specific, AMPR is targeting at recovering an $r$ -rank matrix $\mathbf {M}^*\in \mathbb {R}^{d_1\times d_2}$ as the parametric component from $n$ instantiations/samples of a semi-parametric model $y=f(\langle \mathbf {M}^*, \mathbf {X}\rangle, \epsilon)$ , where the predictor matrix is denoted as $\mathbf {X}\in \mathbb {R}^{d_1\times d_2}$ , link function $f(\cdot, \epsilon)$ is agnostic under some mild distribution assumptions on $\mathbf {X}$ , and $\epsilon$ represents the noise. In this paper, we formulate AMPR as a rank-restricted largest eigenvalue problem by applying the second-order Stein's identity and propose a new spectrum truncation power iteration (STPower) method to obtain the desired matrix efficiently. Also, we show a favorable rank recovery result by adopting the STPower method, i.e., a near-optimal statistical convergence rate under some relatively general model assumption from a wide range of applications. Extensive simulations verify our theoretical analysis and showcase the strength of STPower compared with the other existing counterparts. [ABSTRACT FROM AUTHOR]

In this paper, we consider massive multiple-input-multiple-output (MIMO) communication systems with a uniform planar array (UPA) at the base station (BS) and investigate the downlink precoder design with imperfect channel state information (CSI). By exploiting channel estimates and statistical parameters of channel estimation error, we aim to design precoding vectors to maximize the utility function on the ergodic rates of users subject to a total transmit power constraint. By employing an upper bound of the ergodic rate, we leverage the corresponding Lagrangian formulation and identify the structural characteristics of the optimal precoder as the solution to a generalized eigenvalue problem. The Lagrange multipliers play a crucial role in determining both precoding directions and power parameters, yet are challenging to be solved directly. To figure out the Lagrange multipliers, we develop a general framework underpinned by a properly designed neural network that learns directly from CSI. To further relieve the computational burden, we obtain a low-complexity framework by decomposing the original problem into computationally efficient subproblems with instantaneous and statistical CSI handled separately. With the offline pre-trained neural network, the online computational complexity of precoder is substantially reduced compared with the existing iterative algorithm while maintaining nearly the same performance. [ABSTRACT FROM AUTHOR]

This paper develops an accurate small signal model for line commutated converter based HVDC (LCC-HVDC). The overall process of the model establishment is demonstrated from five parts: AC system, DC system, control system, phase-locked loop (PLL) and the converter. Considering the limitations of the traditional converter equations, the proposed small signal model takes the commutation process into account so that the overlap angle and AC current are calculated with the actual value rather than the estimated value. The accuracy of the proposed model is verified both in the time-domain simulation in PSCAD/EMTDC and by eigenvalue analysis. The results show better performance than the traditional modeling methods, which provides valuable guidance for future LCC-HVDC project design. [ABSTRACT FROM AUTHOR]

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector corresponding to the smallest, or zero, eigenvalue of a matrix representing a linear system. Incorporating this in deep learning frameworks would allow us to explicitly encode known notions of geometry, instead of having the network implicitly learn them from data. However, performing eigendecomposition within a network requires the ability to differentiate this operation. While theoretically doable, this introduces numerical instability in the optimization process in practice. In this paper, we introduce an eigendecomposition-free approach to training a deep network whose loss depends on the eigenvector corresponding to a zero eigenvalue of a matrix predicted by the network. We demonstrate that our approach is much more robust than explicit differentiation of the eigendecomposition using two general tasks, outlier rejection and denoising, with several practical examples including wide-baseline stereo, the perspective-n-point problem, and ellipse fitting. Empirically, our method has better convergence properties and yields state-of-the-art results. [ABSTRACT FROM AUTHOR]

Time delays are inevitable in the power systems with wide-area control signals, which may compromise the control pe-rformance and thus jeopardize the stability of the power systems. To analyze the impacts of system parameters on critical oscillation modes of a time-delayed power system (TDPS), a new method for eigenvalue trajectory tracking of TDPS is proposed in this paper based on the continuation theory of invariant subspaces. When small changes are imposed on system parameters, such as parameters of wide-area damping controllers (WADCs) and time delays, the invariant subspaces are continuously predicted and corrected, followed by the eigenvalues and eigenvectors. In the process, the predictor and corrector are computed by solving linear equations sparsely and in blocks, which is highly scalable and computationally efficient for large-scale power system applications. The 16-generator 68-bus test system and two real-world power grids in China are used to test and demonstrate the proposed method. The results show that the proposed method can accurately and efficiently track eigenvalue trajectories for TDPS, especially for large-scale power grids. In addition, the sensitivities of eigenvalues and eigenvectors with respect to WADCs’ parameters and time delays are obtained as by-products of the approach. [ABSTRACT FROM AUTHOR]

This paper develops a fully distributed self-triggered framework for achieving the second-order consensus in multiagent systems. In this framework, a fully distributed self-triggered scheme is proposed to schedule information transmission for each communication channel. Thus, the communication frequency of each channel is significantly reduced. Here, communication over different channels is independent with each other and, thus, a channel-based control protocol is further proposed. The update times of control protocol could be also lowered in this framework. Here, an iterative evaluation method is constructed to design a fully distributed self-triggered scheme without involving any global information, especially the eigenvalue information of the Laplacian matrix. In addition, by introducing several variables, some sufficient conditions for achieving the second-order consensus and average consensus are obtained, respectively, in a distributed fashion, and the Zeno behavior is successfully eliminated. Finally, a simulation example is provided to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper introduces a node-asynchronous communication protocol in which an agent in a network wakes up randomly and independently, collects states of its neighbors, updates its own state, and then broadcasts back to its neighbors. This protocol differs from consensus algorithms and it allows distributed computation of an arbitrary eigenvector of the network, in which communication between agents is allowed to be directed. (The graph operator is still required to be a normal matrix). To analyze the scheme, this paper studies a random asynchronous variant of the power iteration. Under this random asynchronous model, an initial signal is proven to converge to an eigenvector of eigenvalue 1 (a fixed point) even in the case of operator having spectral radius larger than unity. The rate of convergence is shown to depend not only on the eigenvalue gap but also on the eigenspace geometry of the operator as well as the amount of asynchronicity of the updates. In particular, the convergence region for the eigenvalues gets larger as the updates get less synchronous. Random asynchronous updates are also interpreted from the graph signal perspective, and it is shown that a non-smooth signal converges to the smoothest signal under the random model. When the eigenvalues are real, second order polynomials are used to achieve convergence to an arbitrary eigenvector of the operator. Using second order polynomials the paper formalizes the node-asynchronous communication model. As an application, the protocol is used to compute the Fiedler vector of a network to achieve autonomous clustering. [ABSTRACT FROM AUTHOR]

This paper introduces a dynamic phasor model of a half-bridge modular multilevel converter based on variables in the stationary ABC frame. The application of the dynamic phasor theory makes it possible to use converter eigenvalues to study the effect of steady-state harmonics present in the modular multilevel converter (MMC) on its small-signal stability, since the model is inherently time invariant. Relying on a linear transformation, this paper uses a new set of variables with a modified frequency content, which results in lower order dynamic phasor models. A nonlinear dynamic phasor model is developed and linearized. The linear model is compared with a nonlinear averaged MMC model in time domain. Stability analysis by means of eigenvalues and participation factors is carried out for dynamic phasor models that include different frequency content, and the effect of the circulating current suppression controller is analyzed. [ABSTRACT FROM AUTHOR]

This paper presents an efficient approach to enforce passivity of rational-based fitted systems. The origin of non-passivity is thoroughly reviewed and analyzed. The proposed approach identifies and modifies, from the original non-passive rational approximation, only the partial fractions that generate passivity violations. It is shown in this paper that these partial fractions generally correspond to out-of-band poles. As for proper-type rational approximations, a new method is proposed to force the constant matrix to be positive-definite. The proposed approach is verified via three case studies with highly non-passive conditions. [ABSTRACT FROM AUTHOR]

Analog least mean square (ALMS) loop is a promising method to cancel self-interference (SI) in in-band full-duplex (IBFD) systems. In this paper, the steady state analyses of the residual SI powers in both analog and digital domains are firstly derived. The eigenvalue decomposition is then utilized to investigate the frequency domain characteristics of the ALMS loop. Our frequency domain analyses prove that the ALMS loop has an effect of amplifying the frequency components of the residual SI at the edges of the signal spectrum in the analog domain. However, the matched filter in the receiver chain will reduce this effect, resulting in a significant improvement of the interference suppression ratio (ISR). It means that the SI will be significantly suppressed in the digital domain before information data detection. This paper also derives the lower bounds of ISRs given by the ALMS loop in both analog and digital domains. These lower bounds are joint effects of the loop gain, tap delay, number of taps, and transmitted signal properties. The discovered relationship among these parameters allows the flexibility in choosing appropriate parameters when designing the IBFD systems under given constraints. [ABSTRACT FROM AUTHOR]

In this paper, the conditions of the existence of backward-wave modes in closed, lossless waveguides filled with inhomogeneous and anisotropic medium that has coupling between transverse and longitudinal field components are presented. In these waveguides, Maxwell’s equations are transformed into an infinite linear algebraic equation system by application of the Galerkin version of moment method. Propagation constants of the problem are found as the eigenvalues of the coefficient matrix of this infinite linear algebraic equation system. In this paper, the derivative of the eigenvalue is obtained analytically using the result expressions of moment method and group velocity is determined. It is utilized to reveal necessary and sufficient conditions for the existence of backward-wave mode. These conditions are adequate to determine whether this waveguide supports the backward-wave mode in a frequency range of interest. [ABSTRACT FROM AUTHOR]

Sparse principal component analysis has become one of the most widely used techniques for dimensionality reduction in high-dimensional datasets. While many methods are available for point estimation of eigenstructure in high-dimensional settings, in this paper we propose methodology for uncertainty quantification, such as construction of confidence intervals and tests for the principal eigenvector and the corresponding largest eigenvalue. We base our methodology on an M-estimator with Lasso penalty which achieves minimax optimal rates and is used to construct a de-biased sparse PCA estimator. The novel estimator has a Gaussian limiting distribution and can be used for hypothesis testing or support recovery of the first eigenvector. The empirical performance of the new estimator is demonstrated on synthetic data and we also show that the estimator compares favourably with the classical PCA in moderately high-dimensional regimes. [ABSTRACT FROM AUTHOR]

This paper studies the event-triggered containment control (CC) problem of multiagent systems with a directed graph, where the followers’ communication graph is an undirected graph. A novel event-triggered CC protocol is presented to schedule communications between agents, which depends on both local states and control inputs. Different from traditional approaches using broadcasts, a unique property of the proposed protocol is that it enables agent-to-agent data transmission. To do so, each communication link is associated with a specific local event. The estimated relative interagent states are transmitted over a specific link only when the related input-based event is detected. We develop sufficient conditions to solve CC problem under this protocol and extend it to the adaptive event-triggered protocol that does not require the global knowledge on the smallest positive eigenvalue of the Laplacian. For both protocols, we derive positive low bounds on the interevent time intervals generated by individual events, which eliminate the “Zeno phenomenon.” Feasibility of the proposed algorithm is verified by an example. [ABSTRACT FROM AUTHOR]

As in grid-tied Modular Multilevel Converters (MMC), the steady-state operation under asymmetric grid conditions is rather general, especially for the overhead line of the AC network. Therefore, the small-signal dynamics of MMC under unbalanced grid conditions have become a great important research topic. In this paper, the inherent periodic time-varying characteristic of MMC's original relationships is given priority consideration. Based on the linear time-periodic (LTP) method, a general small-signal LTP model under unbalanced grid conditions is built considering the internal dynamic of submodules (SMs). Then based on the eigenvalue locus analysis method from Floquet- Lyapunov theory, the effects of controller parameters and interactions between different controllers on small-signal dynamics are studied, respectively. Finally, the results from the detailed nonlinear MMC model are provided to verify the effectiveness of the proposed analysis. [ABSTRACT FROM AUTHOR]

Pinning control of a complex network aims at forcing the states of all nodes to track an external signal by controlling a small number of nodes in the network. In this paper, an algebraic graph-theoretic condition is introduced to optimize pinning control. When individual node dynamics and coupling strength of the network are given, the effectiveness of pinning scheme can be measured by the smallest eigenvalue of the grounded Laplacian matrix obtained by deleting the rows and columns corresponding to the pinned nodes from the Laplacian matrix of the network. The larger this smallest eigenvalue, the more effective the pinning scheme. Spectral properties of the smallest eigenvalue are analyzed using the network topology information, including the spectrum of the network Laplacian matrix, the minimal degree of uncontrolled nodes, the number of edges between the controlled node set and the uncontrolled node set, etc. The identified properties are shown effective for optimizing the pinning control strategy, as demonstrated by illustrative examples. Finally, for both scale-free and small-world networks, in order to maximize their corresponding smallest eigenvalues, it is better to pin the nodes with large degrees when the percentage of pinned nodes is relatively small, while it is better to pin nodes with small degrees when the percentage is relatively large. This surprising phenomenon can be explained by one of the theorems established. [ABSTRACT FROM AUTHOR]

An analytic parahermitian matrix admits an eigenvalue decomposition (EVD) with analytic eigenvalues and eigenvectors except in the case of multiplexed data. In this paper, we propose an iterative algorithm for the estimation of the analytic eigenvalues. Since these are generally transcendental, we find a polynomial approximation with a defined error. Our approach operates in the discrete Fourier transform (DFT) domain and for every DFT length generates a maximally smooth association through EVDs evaluated in DFT bins; an outer loop iteratively grows the DFT order and is shown, in general, to converge to the analytic eigenvalues. In simulations, we compare our results to existing approaches. [ABSTRACT FROM AUTHOR]

A highly popular regularized (shrinkage) covariance matrix estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward the grand mean of the eigenvalues of the SCM. In this paper, a more general approach is considered in which the SCM is replaced by an M-estimator of scatter matrix and a fully automatic data adaptive method to compute the optimal shrinkage parameter with minimum mean squared error is proposed. Our approach permits the use of any weight function such as Gaussian, Huber's, Tyler's, or t weight functions, all of which are commonly used in M-estimation framework. Our simulation examples illustrate that shrinkage M-estimators based on the proposed optimal tuning combined with robust weight function do not loose in performance to shrinkage SCM estimator when the data is Gaussian, but provide significantly improved performance when the data is sampled from an unspecified heavy-tailed elliptically symmetric distribution. Also, real-world and synthetic stock market data validate the performance of the proposed method in practical applications. [ABSTRACT FROM AUTHOR]

Subsynchronous control interaction (SSCI) is the interaction between the power-electronics control and the series-compensated transmission system that occurs at frequencies below the system nominal frequency. SSCI may occur between the doubly-fed induction generator (DFIG) control system and the series-compensated transmission line, to which the wind park (WP) is connected. Not only do the DFIG control system parameters, but also the WP operating conditions have a significant impact on SSCI. In this paper, the impact of WP operating conditions and DFIG control system parameters on SSCI is analyzed in detail. Guidelines are presented for modifying the DFIG control system parameters to ensure safe operation and acceptable transient responses due to faults. This paper also examines the accuracies of various analytical tools used for SSCI problem identification and proposes a new frequency scan analysis approach for accurate prediction of potential SSCI problems. [ABSTRACT FROM PUBLISHER]

This paper presents a method for small-signal dynamic studies of power systems including utility-scale PV energy systems considering the effects of dc-side components. Existing methods commonly model a PV energy system as a dc source connected to a grid-tied inverter. This paper shows that the dc components of a PV energy system can also contribute in the dynamics of the power system in the range of small-signal studies. The paper first develops the model of a PV energy system by merging the submodels of dc- and ac-side components. Then, a method to obtain the augmented model of the power system including a PV energy system will be explained using a study system. The study system consists of a PV energy system in parallel with a synchronous generator connected to a grid. Then, based on eigenvalue analysis, verified by time-domain simulations, it is shown that the dc-link capacitor, front-end converter, and its controller can introduce oscillatory modes in subsynchronous range of frequencies. Furthermore, it is shown that the damping of the sensitive modes can significantly vary with respect to the parameters of the dc-side components. [ABSTRACT FROM PUBLISHER]

The paper presents a comprehensive study of small-signal stability analysis of power systems based on matrix pencils and the generalized eigenvalue problem. Both primal and dual formulations of the generalized eigenvalue problem are considered and solved through a variety of state-of-the-art solvers. The paper also discusses the impact on the performance of the solvers of two formulations of the equations modelling the power systems, namely, the explicit and semi-implicit form of differential-algebraic equations. The case study illustrates the theoretical aspects and numerical features of these formulations and solvers through two real-world systems, namely, a 1,479-bus model of the all-island Irish system, and a 21,177-bus model of the ENTSO-E network. [ABSTRACT FROM PUBLISHER]

This paper investigates the small-signal stability of power electronics-based power systems in frequency domain. A comparison between the impedance-based and the eigenvalue-based stability analysis methods is presented. A relation between the characteristics equation of the eigenvalues and poles and zeros of the minor-loop gain from the impedance-based analysis have been derived analytically. It is shown that both stability analysis methods can effectively determine the stability of the system. In the case of the impedance-based method, a low phase-margin in the Nyquist plot of the minor-loop gain indicates that the system can exhibit harmonic oscillations. A weakness of the impedance method is the limited observability of certain states given its dependence on the definition of local source-load subsystems, which makes it necessary to investigate the stability at different subsystems. To address this limitation, the paper discusses critical locations where the application of the method can reveal the impact of a passive component or a controller gain on the stability. On the other hand, the eigenvalue-based method, being global, can determine the stability of the entire system; however, it cannot unambiguously predict sustained harmonic oscillations in voltage source converter (VSC) based high voltage dc (HVdc) systems caused by pulse-width modulation (PWM) switching. To generalize the observations, the two methods have been applied to dc–dc converters. To illustrate the difference and the relation between the two-methods, the two stability analysis methods are then applied to a two-terminal VSC-based HVdc system as an example of power electronics-based power systems, and the theoretical analysis has been further validated by simulation and experiments. [ABSTRACT FROM AUTHOR]

This paper presents a novel day-and-night control of large PV solar farm as STATCOM, termed PV-STATCOM, for FIDVR alleviation. The proposed control involves dynamic modulation of both reactive and real power during day, and of reactive power during night. The active and reactive power output of solar farm are based on the sensitivity of solar plant voltage to active and reactive power injections. Enhanced voltage control up to utility Transient Overvoltage Limit is utilized. Eigenvalue analysis is done to study the sensitivity of proposed controller performance to various power system and PV plant parameters. Extensive PSCAD simulation studies of FIDVR are performed in a realistic power transmission system with large-scale PV plant and comprehensive IM loads. It is shown that the proposed PV-STATCOM control: (i) mitigates FIDVR even if solar farm is located more than 100 km from motor loads, (ii) is more effective than reactive power support required by German Grid Code, (iii) is equally effective as a STATCOM connected locally at motor loads, and (iv) stabilizes motors at night which is beyond Grid Code requirements. The PV-STATCOM potentially provides significant cost savings to utilities and new revenue stream for solar plants in providing 24/7 FIDVR mitigation service. [ABSTRACT FROM AUTHOR]

Power system state estimation is heavily subjected to measurement error, which comes from the noise of measuring instruments, communication noise, and some unclear randomness. Traditional weighted least square (WLS), as the most universal state estimation method, attempts to minimize the residual between measurements and the estimation of measured variables, but it is unable to handle the measurement error. To solve this problem, based on random matrix theory, this paper proposes a data-driven approach to clean measurement error in matrix-level. Our method significantly reduces the negative effect of measurement error, and conducts a two-stage state estimation scheme combined with WLS. In this method, a Hermitian matrix is constructed to establish an invertible relationship between the eigenvalues of measurements and their covariance matrix. Random matrix tools, combined with an optimization scheme, are used to clean measurement error by shrinking the eigenvalues of the covariance matrix. With great robustness and generality, our approach is particularly suitable for large interconnected power grids. Our method has been numerically evaluated using different testing systems, multiple models of measured noise and matrix size ratios. [ABSTRACT FROM AUTHOR]

This paper presents a fast and efficient alternative method to enforce passivity of frequency-dependent network equivalents (FDNE). Based on the eigenvalue perturbation theory, the proposed technique relocates the eigenvalues of the half-size singularity matrix by iteratively perturbing the residues of the FDNE model until the rational function becomes passive. It is demonstrated that the proposed technique achieves significant computational savings compared to traditional techniques. Three illustrative case studies involving different conditions of passivity violations are presented to validate the proposed method. Its effectiveness is demonstrated via comparison with two commonly used techniques, i.e., Fast Residue Perturbation (FRP) and Hamiltonian Matrix Perturbation (HMP). [ABSTRACT FROM AUTHOR]

Principal skewness analysis (PSA) has been introduced for feature extraction in hyperspectral imagery. As a third-order generalization of principal component analysis (PCA), its solution of searching for the local maximum skewness direction is transformed into the problem of calculating the eigenpairs (the eigenvalues and the corresponding eigenvectors) of a coskewness tensor. By combining a fixed-point method with an orthogonal constraint, the new eigenpairs are prevented from converging to the same previously determined maxima. However, in general, the eigenvectors of the supersymmetric tensor are not inherently orthogonal, which implies that the results obtained by the search strategy used in PSA may unavoidably deviate from the actual eigenpairs. In this paper, we propose a new nonorthogonal search strategy to solve this problem and the new algorithm is named nonorthogonal principal skewness analysis (NPSA). The contribution of NPSA lies in the finding that the search space of the eigenvector to be determined can be enlarged by using the orthogonal complement of the Kronecker product of the previous eigenvector with itself, instead of its orthogonal complement space. We also give a detailed theoretical proof on why we can obtain the more accurate eigenpairs through the new search strategy by comparison with PSA. In addition, after some algebraic derivations, the complexity of the presented algorithm is also greatly reduced. Experiments with both simulated data and real multi/hyperspectral imagery demonstrate its validity in feature extraction. [ABSTRACT FROM AUTHOR]

Invisible units mainly refer to small-scale units that are not monitored by, and thus are not visible to utilities. Integration of these invisible units into power systems does significantly affect the way in which a distribution grid is planned and operated. This paper, based on random matrix theory (RMT), proposes a statistical, data-driven framework to handle the massive grid data, in contrast to its deterministic, model-based counterpart. Combining the RMT-based data-mining framework with conventional techniques, some heuristics are derived as the solution to the invisible units detection and estimation task: linear eigenvalue statistic indicators (LESs) are suggested as the main ingredients of the solution; according to the statistical properties of LESs, the hypothesis testing is formulated to conduct change point detection in the high-dimensional space. The proposed method is promising for anomaly detection and pertinent to current distribution networks—it is capable of detecting invisible power usage and fraudulent behavior while even being able to locate the suspect's location. Case studies, using both simulated data and actual data, validate the proposed method. [ABSTRACT FROM AUTHOR]

This paper considers leader-following bipartite consensus of single-integrator multiagent systems in the presence of measurement noise. To attenuate the noise, a time-varying consensus gain ${q}$ (${t}$) is introduced into the stochastic approximation-type protocol. Necessary and sufficient conditions for ensuring a strong mean square leader-following bipartite consensus are given. In particular, in the absence of measurement noise, the convergence speed of error dynamics is dependent on the eigenvalues of Laplacian and the rate of ${\int ^{{t}}_{0}{q}({s})\text {d}{s}}$ approaching infinity. By appropriately choosing ${q}$ (${t}$), the speed of leader-following bipartite consensus convergence can be improved in a fixed communication topology. It is proven that conditions for the signed digraph to be structurally balanced and having a spanning tree are necessary and sufficient to ensure leader-following bipartite consensus, regardless of measurement noise. [ABSTRACT FROM AUTHOR]

The existing spectral discretization-based methods (SDMs) are capable of accurately computing critical eigenvalues of large power systems when time delays in wide-area damping control loops are considered. However, SDMs suffer from huge dimension of the discretized matrices of spectral operators, which is usually dozens of times of actual system states. To resolve the problem, an idea of partial spectral discretization (PSD) is proposed in this paper where only the retarded state variables instead of all system states are discretized. Following the PSD idea, a partial and explicit infinitesimal generator discretization (PEIGD) method is presented for highly efficient eigen-analysis of large closed-loop delayed cyber-physical power system (DCPPS). In contrast to the original EIGD method, the order of the resultant discretized matrix of the infinitesimal generator is greatly reduced and close to the number of actual state variables. The computational burden of PEIGD can be an order of magnitude less than that of EIGD and nearly the same as eigen-analysis of a system without time delay. Moreover, PEIGD is endowed with exactly the same accuracy as EIGD in capturing critical oscillation modes. Both theoretical analyses and intensive tests on the 16-generator 68-bus test system as well as a 516-bus and a 33028-bus real-life large power systems verify the accuracy and efficiency of the presented method. [ABSTRACT FROM AUTHOR]

Randomness extraction against side information is the art of distilling from a given source a key which is almost uniform conditioned on the side information. This paper provides randomness extraction against quantum side information whose extractable key length is given by a quantum generalization of the collision entropy, which is smoothed and conditioned differently from how this is done in existing schemes. Based on the fact that the collision entropy is not subadditive, its optimization with respect to additional side information is introduced, and is shown to be asymptotically optimal. The lower bound derived there for general states is expressed as the difference between two unconditional entropies and its evaluation reduces to an eigenvalue problem of two states, which are the entire state and the marginal state of side information. [ABSTRACT FROM AUTHOR]