The stability analysis of islanded inverter-based microgrids (IBMGs) is increasingly an important and challenging topic due to the nonlinearity of IBMGs. In this paper, a new linear model for such microgrids as well as an iterative method to correct the linear model is proposed. Using the linear model makes it easy to analyze the eigenvalues and stability of IBMGs due to the fact that it derive...

In this paper, we analyze conditions under which the spectrum of Sturm–Liouville operator on a certain smooth curve is localized near countable number rays. case where potential piecewise analytical, an asymptotic eigenvalues found for each series corresponding ray. The result obtained allows one to generalize well-known formula distribution function stated by Davies in finite localization

We compute the quantum correction δA due to weak localization for transport properties A = ∑ n a(Tn) of disordered quasi-one-dimensional conductors, by integrating the Dorokhov-Mello-Pereyra-Kumar equation for the distribution of the transmission eigenvalues Tn. The result δA = (1 − 2/β)[ 1 4 a(1) + ∫∞ 0 dx (4x + π2)−1a(cosh x)] is independent of sample length or mean free path, and has a unive...

In this paper, we study the fluctuations of the extreme eigenvalues of a spiked finite rank deformation of a Hermitian (resp. symmetric) Wigner matrix when these eigenvalues separate from the bulk. We exhibit quite general situations that will give rise to universality or non universality of the fluctuations, according to the delocalization or localization of the eigenvectors of the perturbatio...

We study the localization properties of eigenvectors of the Google matrix, generated both from the world wide web and from the Albert-Barabási model of networks. We establish the emergence of a delocalization phase for the PageRank vector when network parameters are changed. For networks with localized PageRank, eigenvalues of the matrix in the complex plane with a modulus above a certain thres...

From density-functional calculations, we show that localized states stemming from defects or topological disorder exhibit an anomalously large electron–phonon coupling. We provide a simple analysis to explain the observation and perform a detailed study on an interesting system: amorphous silicon. We compute firstprinciples deformation potentials (by computing the sensitivity of specific electr...

We present an analytical method for finding all the electronic eigenfunctions and eigenvalues of the aperiodic Thue-Morse lattice. We prove that this system supports only extended electronic states which is a very unusual behavior for this class of systems, and so far as we know, this is the only example of a quasiperiodic or aperiodic system in which critical or localized states are totally ab...

We study a generalized Aubry-Andre model that obeys $\mathcal{PT}$-symmetry. observe robust $\mathcal{PT}$-symmetric phase with respect to system size and disorder strength, where all eigenvalues are real despite the Hamiltonian being non-hermitian. This can support an Anderson localization transition, giving rich diagram as result of interplay between Our provides perfect platform disorder-dri...

We propose a new method for finding discrete eigenvalues the direct Zakharov-Shabat problem, based on moving in complex plane along argument jumps of function a(?), localization which does not require great accuracy. It allows to find all taking into account their multiplicity faster than matrix methods and contour integrals. The shows significant advantage over other when calculating large spe...

the stability analysis of islanded inverter-based microgrids (ibmgs) is increasingly an important and challenging topic due to the nonlinearity of ibmgs. in this paper, a new linear model for such microgrids as well as an iterative method to correct the linear model is proposed. using the linear model makes it easy to analyze the eigenvalues and stability of ibmgs due to the fact that it derive...