A pole-free modal field-matching technique for eigenvalue problems in electromagnetics

The use of the minimum singular value (MSV) of the load flow Jacobian has been proposed as a security index for monitoring how close the operating condition of a power system is to a voltage instability. However, direct computation of singular value decomposition (SVD) is a very time consuming task. P.A. Lof et al. (see IEEE Trans. on Power Systems, vol.7, no.1, p.54-64, 1992) report on an elegant and an efficient algorithm for the computation of the MSV of the load flow Jacobian matrix (LFJM). This algorithm greatly reduces the time required for the computation of the MSV. In this letter, a new starting condition that reduces the computation time for the iterative process described by Lof et al. is proposed.

When the system reaches the static voltage stability limit point, Jacobian matrix is singular. By checking if minimum singular value is zero, its very easy to determine whether or not Jacobian matrix is singular. So the minimum singular value of Jacobian matrix can reflects the degree of system voltage stability effectively. Firstly this paper introduces singular value decomposition, analyses load characteristic and excitation limits involved in this method and examples on PSD-FDS are demonstrated. At last, suggestion on voltage stability monitoring by minimum singular value is proposed.

Given m square matrices A/sub 1/, ..., A/sub m/, let A denote the set of all their convex combinations. Then the authors consider the problem of determining a member of A whose minimum singular value is the smallest. A related problem, known as robust nonsingularity problem, is to determine if every member of A is nonsingular. Clearly a solution to the authors' problem automatically solves the robust nonsingularity problem. Unfortunately, the robust nonsingularity problem has been demonstrated to be NP-hard which in turn makes the authors' problem NP-hard. To avoid this computational intractability, the authors provide an algorithm that computes a lower bound and an upper bound on the least minimum singular value within a prescribed tolerance. Of course, if the prescribed tolerance is set to zero then the authors' algorithm would compute the least minimum singular value. The authors' method makes use of the so-called simplicial algorithms. >

Aiming at the problem of singular configuration of industrial robot in linear operation, this paper analyzes and studies the singularity configuration and singularity avoidance method of industrial robot, and a dynamic damping least square method singularity avoidance trajectory planning algorithm based on minimum singular value is proposed. The kinematics model of the robot with spherical wrist structure is established. Based on the decoupling analysis of the robot singularity, the singularity mathematical expressions of the wrist, the elbow and the shoulder are obtained respectively. It is closely related to the length and offset of connecting link. The dynamic damped least square method based on the minimum singular value is used to adjust the trajectory of the Cartesian space and the mapped joint space in the singular region. Simulation results show that the velocity of the proposed method is stable near the singular configuration, and there is no uncontrollable phenomenon of motion discontinuity and stability degradation.

UPFC control parameter identification for effective power oscillation damping

The main purpose of this paper is to investigate the perturbation bounds of the tensor eigenvalue and singular value problems with even order. We extend classical definitions from matrices to tensors, such as, -tensor and the tensor polynomial eigenvalue problem. We design a method for obtaining a mode-symmetric embedding from a general tensor. For a given tensor, if the tensor is mode-symmetric, then we derive perturbation bounds on an algebraic simple eigenvalue and Z-eigenvalue. Otherwise, based on symmetric or mode-symmetric embedding, perturbation bounds of an algebraic simple singular value are presented. For a given tensor tuple, if all tensors in this tuple are mode-symmetric, based on the definition of a -tensor, we estimate perturbation bounds of an algebraic simple polynomial eigenvalue. In particular, we focus on tensor generalized eigenvalue problems and tensor quadratic eigenvalue problems.

In this paper the static voltage stability index has been identified by minimum singular value of the power flow jacobian matrix. The system security in power system models by the scalar magnitude of a voltage stability index may be a very difficult task. When we are taking account of reactive power generation limits it is very difficult to predict stability index at voltage collapse points. Here a quick method is used to calculate the minimum singular value and the corresponding left and right singular vectors are presented. This developed algorithm is very useful in online because it required small amount of computation time. For different patterns of load and generation are increases, to determine voltage collapse point. For solving the maximum loading problem an optimal power flow approach was used with these points the MSV is calculated and used for training and testing the Neural Network.

In this work we examine the behavior of the minimum singular value of random Vandermonde matrices. In particular, we prove that the minimum singular value s 1 (N) is at most N exp(−C√N) where N is the dimension of the matrix and C is a constant. Furthermore, the value of the constant C is determined explicitly. The main result is obtained in two different ways. One approach uses techniques from stochastic processes and in particular, a construction related to the Brownian bridge. The other one is a more direct analytical approach involving combinatorics and complex analysis. As a consequence, we obtain a lower bound on the maximum absolute value of a random polynomial on the unit circle, which may be of independent mathematical interest.

This paper proposes a method to select the supplementary input signal for systems equipped with static synchronous compensators (STATCOM) to damp inter-area mode(s). Input-output observability-controllability analysis, minimum singular value, right half plane zeros and relative gain array are used to assess the most appropriate supplementary input signal. The open-loop frequency of the system is shown to examine the sensitivity of the selected supplementary input signal to inter-area mode. The method is applied to select the input signal for a small power system equipped with a single STATCOM and for a large power system equipped with two STATCOMs.

The signal sample tool which is called measurement matrix or observation matrix is very important for the theory of compressive sensing. Decreasing the correlation between any two different columns of the information operator is the basis of the design and optimization of the measurement matrix. Based on it, the non-diagonal elements of the upper triangular matrix of the QR decomposition of information operator was set to zero to increase its minimum singular value and decrease the column correlation of information operator, and thus this method can enhance the performance of the measurement matrix. Experiments illustrate that when the algorithm of this paper is utilized, the recovery error of signals and images are both diminished.

In order to adjust telescope mirrors with high precision, a 3 cylindrical-prismatic-spherical (CPS) parallel micro-manipulator with 6 degrees-of-freedom (DOF) and partial decoupling is proposed. Structure characteristics of the micro-manipulator were analyzed and the kinematic equations were derived based on Euler method. To avoid tedious derivation, Jacobian matrix with screw theory representing the input and output relation of micro-manipulator is established by using velocity influence coefficient method. Combining topological structure characteristics of the 3-CPS parallel micro-manipulator, the solving procedures of workspace are obtained. Moreover, the position workspace with a given orientation and the orientation workspace with a given translation position are constructed by numerical simulations. The workspace range is chosen as the optimization goal of structure parameters, and the circumcircle radius ratio of base and moving platform and the lengths of each sub-link are optimized. The maximum condition number and the minimum singular value are chosen as the precision indexes to analyze the precision performance of the workspace. Then, the properties of the position workspaces with various orientations and the orientation workspaces with various positions are simulated numerically, and the simulation results prove that the 3-CPS parallel micro-manipulator has an ability to achieve high precision operations. This research provides a workspace modeling and optimization method for the practical application in telescope mirror adjustment or other fields requiring high precision.

Multi-task learning has been observed by many researchers, which supposes that different tasks can share a low-rank common yet latent subspace. It means learning multiple tasks jointly is better than learning them independently. In this paper, we propose two novel multi-task learning formulations based on two regularization terms, which can learn the optimal shared latent subspace by minimizing the exactly k minimal singular values. The proposed regularization terms are the more tight approximations of rank minimization than trace norm. But it's an NP-hard problem to solve the exact rank minimization problem. Therefore, we design a novel re-weighted based iterative strategy to solve our models, which can tactically handle the exact rank minimization problem by setting a large penalizing parameter. Experimental results on benchmark datasets demonstrate that our methods can correctly recover the low-rank structure shared across tasks, and outperform related multi-task learning methods.

Chapter 3 is devoted to studying the computation efficiency of existing methods for computing focus values. Three typical methods, namely the Poincare method or Takens method, the perturbation technique, and the singular point value method are discussed. These three methods are shown to have the same order of computational complexity; no method has been developed so far for computing the ‘minimal singular point values’.

The classical perturbation theory for Hermitian matrix eigenvalue and singular value problems provides bounds on the absolute differences between approximate eigenvalues (singular values) and the true eigenvalues (singular values) of a matrix. These bounds may be bad news for small eigenvalues (singular values), which thereby suffer worse relative uncertainty than large ones. However, there are situations where even small eigenvalues are determined to high relative accuracy by the data much more accurately than the classical perturbation theory would indicate. In this paper, we study how eigenvalues of a Hermitian matrix A change when it is perturbed to $\wtd A=D^*AD$, where D is close to a unitary matrix, and how singular values of a (nonsquare) matrix B change when it is perturbed to $\wtd B=D_1^*BD_2$, where D1 and D2 are nearly unitary. It is proved that under these kinds of perturbations small eigenvalues (singular values) suffer relative changes no worse than large eigenvalues (singular values). Many well-known perturbation theorems, including the Hoffman--Wielandt and Weyl--Lidskii theorems, are extended.

The paper treats a problem of propagation of electromagnetic symmetric hybrid wave in a plane non-homogeneous nonlinear dielectric waveguide. The physical problem is reduced to a nonlinear transmission eigenvalue problem for Maxwell’s equations with appropriate boundary and transmission conditions. The eigenvalue problem is, in fact, a two-parameter problem, where the spectral parameter depends on another parameter, which is chosen in accordance with special conditions. Uniqueness of solution to the two-parameter eigenvalue problem is proved, numerical method is proposed and numerical results are presented.