Reliability assessment of microgrid with renewable generation and prioritized loads

With the increase in awareness about the climate change, there has been a tremendous shift towards utilizing renewable energy sources (RES). In this regard, smart grid technologies have been presented to facilitate higher penetration of RES. Microgrids are the key components of the smart grids. Microgrids allow integration of various distributed energy resources (DER) such as the distributed generation (DGs) and energy storage systems (ESSs) into the distribution system and hence remove or delay the need for distribution expansion. One of the crucial requirements for utilities is to ensure that the system reliability is maintained with the inclusion of microgrid topology. Therefore, this paper evaluates the reliability of a microgrid containing prioritized loads and distributed RES through a hybrid analytical-simulation method. The stochasticity of RES introduces complexity to the reliability evaluation. The method takes into account the variability of RES through Monte- Carlo state sampling simulation. The results indicate the reliability enhancement of the overall system in the presence of the microgrid topology. In particular, the highest priority load has the largest improvement in the reliability indices. Furthermore, sensitivity analysis is performed to understand the effects of the failure of microgrid islanding in the case of a fault in the upstream network

Energy cost associated with vortex crossing in superconductors

Starting from the Ginzburg-Landau free energy of a type II superconductor in a magnetic field we estimate the energy associated with two vortices crossing. The calculations are performed by assuming that we are in a part of the phase diagram where the lowest Landau level approximation is valid. We consider only two vortices but with two markedly different sets of boundary conditions: on a sphere and on a plane with quasi-periodic boundary conditions. We find that the answers are very similar suggesting that the energy is localised to the crossing point. The crossing energy is found to be field and temperature dependent -- with a value at the experimentally measured melting line of $U_\times \simeq 7.5 k T_m \simeq 1.16/c_L^2$, where $c_L$ is the Lindemann melting criterion parameter. The crossing energy is then used with an extension of the Marchetti, Nelson and Cates hydrodynamic theory to suggest an explanation of the recent transport experiments of Safar {{\em et al.}\ }.Comment: 15 pages, RevTex v3.0, followed by 5 postscript figure

First-Order Melting of a Moving Vortex Lattice: Effects of Disorder

We study the melting of a moving vortex lattice through numerical simulations with the current driven 3D XY model with disorder. We find that there is a first-order phase transition even for large disorder when the corresponding equilibrium transition is continuous. The low temperature phase is an anisotropic moving glass.Comment: Important changes from original version. Finite size analysis of results has been added. Figure 2 has been changed. There is a new additional Figure. To be published in Physical Review Letter

First-Order Vortex Lattice Melting and Magnetization of YBa2_2Cu3_3O$_{7-\delta}

We present the first non-mean-field calculation of the magnetization $M(T)$ of YBa$_2$Cu$_3$O$_{7-\delta}$ both above and below the flux-lattice melting temperature $T_m(H)$. The results are in good agreement with experiment as a function of transverse applied field $H$. The effects of fluctuations in both order parameter $\psi({\bf r})$ and magnetic induction $B$ are included in the Ginzburg-Landau free energy functional: $\psi({\bf r})$ fluctuates within the lowest Landau level in each layer, while $B$ fluctuates uniformly according to the appropriate Boltzmann factor. The second derivative $(\partial^2 M/\partial T^2)_H$ is predicted to be negative throughout the vortex liquid state and positive in the solid state. The discontinuities in entropy and magnetization at melting are calculated to be $\sim 0.034\, k_B$ per flux line per layer and $\sim 0.0014$~emu~cm$^{-3}$ at a field of 50 kOe.Comment: 11 pages, 4 PostScript figures in one uuencoded fil

Non-Hermitian Delocalization and Eigenfunctions

Recent literature on delocalization in non-Hermitian systems has stressed criteria based on sensitivity of eigenvalues to boundary conditions and the existence of a non-zero current. We emphasize here that delocalization also shows up clearly in eigenfunctions, provided one studies the product of left- and right-eigenfunctions, as required on physical grounds, and not simply the squared modulii of the eigenfunctions themselves. We also discuss the right- and left-eigenfunctions of the ground state in the delocalized regime and suggest that the behavior of these functions, when considered separately, may be viewed as ``intermediate'' between localized and delocalized.Comment: 8 pages, 11 figures include

Superconducting zero temperature phase transition in two dimensions and in the magnetic field

We derive the Ginzburg-Landau-Wilson theory for the superconducting phase transition in two dimensions and in the magnetic field. Without disorder the theory describes a fluctuation induced first-order quantum phase transition into the Abrikosov lattice. We propose a phenomenological criterion for determining the transition field and discuss the qualitative effects of disorder. Comparison with recent experiments on MoGe films is discussed.Comment: 7 pages, 2 figure

Vortex shear effects in layered superconductors

Motivated by recent transport and magnetization measurements in BSCCO samples [B. Khaykovich et. al., Phys. Rev. B 61, R9261 (2000)], we present a simple macroscopic model describing effects of inhomogeneous current distribution and shear in a layered superconductor. Parameters of the model are deduced from a microscopic calculation. Our model accounts for the strong current non-linearities and the re-entrant temperature dependence observed in the experiment.Comment: 11 pages, 7 figures, submitted to Phys. Rev.

Plastic energies in layered superconductors

We estimate the energy cost associated with two pancake vortices colliding in a layered superconductor. It is argued that this energy sets the plastics energy scale and is the analogue of the crossing energy for vortices in the continuum case. The starting point of the calculation is the Lawrence-Doniach version of the Ginzburg-Landau free energy for type-II superconductors. The magnetic fields considered are along the c-direction and assumed to be sufficiently high that the lowest Landau level approximation is valid. For Bi-2212, where it is know that layering is very important, the results are radically different from what would have been obtained using a three-dimensional anisotropic continuum model. We then use the plastic energy for Bi-2212 to successfully explain recent results from Hellerqvist {\em et al.}\ on its longitudinal resistance.Comment: 5 Pages Revtex, 4 uuencoded postscript figure

Supercooling of the disordered vortex lattice in Bi_2Sr_2CaCu_2O_8+d

Time-resolved local induction measurements near to the vortex lattice order-disorder transition in optimally doped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ single crystals shows that the high-field, disordered phase can be quenched to fields as low as half the transition field. Over an important range of fields, the electrodynamical behavior of the vortex system is governed by the co-existence of the two phases in the sample. We interpret the results in terms of supercooling of the high-field phase and the possible first order nature of the order-disorder transition at the ``second peak''.Comment: 4 pages, 3 figures. Submitted to Nature, July 10th, 1999; Rejected August 8th for lack of broad interest Submitted to Physical Review Letters September 10th, 199

Superfluid-insulator transition of the Josephson junction array model with commensurate frustration

We have studied the rationally frustrated Josephson-junction array model in the square lattice through Monte Carlo simulations of $(2+1)$D XY-model. For frustration $f=1/4$, the model at zero temperature shows a continuous superfluid-insulator transition. From the measurement of the correlation function and the superfluid stiffness, we obtain the dynamical critical exponent $z=1.0$ and the correlation length critical exponent $\nu=0.4 \pm 0.05$. While the dynamical critical exponent is the same as that for cases $f=0$, 1/2, and 1/3, the correlation length critical exponent is surprisingly quite different. When $f=1/5$, we have the nature of a first-order transition.Comment: RevTex 4, to appear in PR