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In sparse subspace clustreing (SSC), non‐zero coefficients in the sparse representations are transformed to positive values to construct the affinity matrix. However, negative coefficients are not supposed to cause positive correlation in nature, so that the clustering performance may be undermined. In this Letter, non‐negative SSC by orthogonal matching pursuit (nSSCOMP) with a negative re‐purpose module is introduced for a reasonable clustering graph to improve the clustering performance, also an assemble negatives of negatives algorithm is proposed to strengthen the effectiveness of affinity matrix. The analysis indicates that the authors' approach can make the coefficient matrix contains only non‐negative values and bring additional positive correlations. Their approach is the first to process negative values after sparse representations are already calculated, without specify non‐negativity constraints beforehand. Experimental results demonstrate with the nSSCOMP not only the clustering accuracy and subspace‐preserving property can be improved, but also time complexity be kept. [ABSTRACT FROM AUTHOR]

This study presents a graphical presentation of the harmonic operating principles in voltage source converter (VSC) with sparse vector methods and provides a visualisation method for analysing the harmonic operations of VSC. Based on the dynamic phasor sequence components model of the VSC, the operation analysis of VSC has been transformed into a solution of an algebraic equations. With the sparse characteristics of the vectors and coefficient matrix, the sparse vector method is applied into solving equations. The coupling from the ac‐side to the dc‐side can be represented by the forward substitution operations and the coupling from the dc‐side to the ac‐side can be represented by the back solution operations in the sparse vector method correspondingly. Therefore, the factorisation paths which describe the forward substitution and the back solution operations can describe the harmonic operating principles of VSC too. When the set of factorisation paths are presented as the weighted directed graphs based on graph theory, the harmonic operating principles of VSC can be displayed as the graphs, which is direct and clear. Finally, the simulation results testify the correctness of the studies. [ABSTRACT FROM AUTHOR]

The problem of fault estimation for a class of non‐linear systems with Lipschitzian non‐linearities and faults is studied. In most of the existing fault estimation methods, the coefficient matrix of the fault vector is required to be full column rank, which leads to that the corresponding estimation approaches are conservative and unsuitable commonly for systems with multiple faults or/and subject to disturbances. In this study, this restriction is relaxed. A novel fault estimation method is proposed, where a full‐column‐rank state variable substitution is introduced so as to meet the requirement of fault estimation. The designed estimation observer guarantees the asymptotic stability of the overall error system with a prescribed H ∞ performance. The states and faults can be estimated with good accuracy simultaneously. Then, the proposed estimation approach is further extended to solve the problem of fault estimation for non‐linear systems with multiple faults or/and subject to disturbances. Finally, numerical examples illustrate the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

Consider an infinite dimensional vector linear process. Under suitable assumptions on the parameter space, we provide consistent estimators of the autocovariance matrices. In particular, under causality, this includes the infinite-dimensional vector autoregressive (IVAR) process. In that case, we obtain consistent estimators for the parameter matrices. An explicit expression for the estimators is obtained for IVAR(1), under a fairly realistic parameter space. We also show that under some mild restrictions, the consistent estimator of the marginal large dimensional variance-covariance matrix has the same convergence rate as that in case of i.i.d. samples. [ABSTRACT FROM AUTHOR]

This study presents a quadratic optimal reactive power flow (ORPF) models for ac‐dc hybrid power system. In the ac system, the load tap changing transformer is represented by an ideal transformer and its series impedance with an artificial node located between them. The ideal transformer is further replaced by the current injections at the two terminal nodes. The artificial node voltage and the current injections are used to express the relationship between the quantities at both sides. For the dc system, some variables are introduced to formulate the dc equations. Finally, utilising their couplings, the ac and dc equations expressed in different coordinates can be integrated into a unified quadratic ac‐dc ORPF model, which is simply expressed in the block form. The predictor‐corrector primal‐dual interior‐point method is used to solve the optimisation problem. The quadratic model results in the constant Hessians that all have elements of 1 or −1, and mostly being zero and multiplication is not required to form the full Hessian, thereby accelerating the entire optimal process significantly. Extensive numerical simulations have shown the validity and superior performance of the proposed model than the conventional one. [ABSTRACT FROM AUTHOR]

In this paper, an improved procedure for imposing displacement boundary conditions in the direct stiffness method of the finite element analysis is presented. The proposed procedure neither changes the original order of the master stiffness matrix, nor does it require the rearrangement of the coefficient matrix. Consequently, it is easy to be implemented. Especially, the condition numbers of coefficient matrices of the improved procedure are remarkably reduced; hence the sensitivity of the solution to perturbations is considerably lowered. Numerical examples are used to demonstrate the validity of the proposed procedure. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]