Real-time monitoring of critical nodes with minimal number of Phasor Measurement Units

This paper presents a method for placement of Phasor Measurement Units, ensuring the monitoring of vulnerable buses which are obtained based on transient stability analysis of the overall system. Real-time monitoring of phase angles across different nodes, which indicates the proximity to instability, the very purpose will be well defined if the PMUs are placed at buses which are more vulnerable. The issue is to identify the key buses where the PMUs should be placed when the transient stability prediction is taken into account considering various disturbances. Integer Linear Programming technique with equality and inequality constraints is used to find out the optimal placement set with key buses identified from transient stability analysis. Results on IEEE-14 bus system are presented to illustrate the proposed approach.

Practical Algorithms For Mean Velocity Estimation In Pulse Doppler Weather Radars Using A Small Number Of Samples

Doppler weather radars with fast scanning rates must estimate spectral moments based on a small number of echo samples. This paper concerns the estimation of mean Doppler velocity in a coherent radar using a short complex time series. Specific results are presented based on 16 samples. A wide range of signal-to-noise ratios are considered, and attention is given to ease of implementation. It is shown that FFT estimators fare poorly in low SNR and/or high spectrum-width situations. Several variants of a vector pulse-pair processor are postulated and an algorithm is developed for the resolution of phase angle ambiguity. This processor is found to be better than conventional processors at very low SNR values. A feasible approximation to the maximum entropy estimator is derived as well as a technique utilizing the maximization of the periodogram. It is found that a vector pulse-pair processor operating with four lags for clear air observation and a single lag (pulse-pair mode) for storm observation may be a good way to estimate Doppler velocities over the entire gamut of weather phenomena.

Design of speaker identification schemes for large number of speakers (A)

Design of speaker identification schemes for a small number of speakers (around 10) with a high degree of accuracy in controlled environment is a practical proposition today. When the number of speakers is large (say 50–100), many of these schemes cannot be directly extended, as both recognition error and computation time increase monotonically with population size. The feature selection problem is also complex for such schemes. Though there were earlier attempts to rank order features based on statistical distance measures, it has been observed only recently that the best two independent measurements are not the same as the combination in two's for pattern classification. We propose here a systematic approach to the problem using the decision tree or hierarchical classifier with the following objectives: (1) Design of optimal policy at each node of the tree given the tree structure i.e., the tree skeleton and the features to be used at each node. (2) Determination of the optimal feature measurement and decision policy given only the tree skeleton. Applicability of optimization procedures such as dynamic programming in the design of such trees is studied. The experimental results deal with the design of a 50 speaker identification scheme based on this approach.

Stability and throughput analysis of unslotted CDMA-ALOHA with finite number of users and code sharing

We consider a system comprising a finite number of nodes, with infinite packet buffers, that use unslotted ALOHA with Code Division Multiple Access (CDMA) to share a channel for transmitting packetised data. We propose a simple model for packet transmission and retransmission at each node, and show that saturation throughput in this model yields a sufficient condition for the stability of the packet buffers; we interpret this as the capacity of the access method. We calculate and compare the capacities of CDMA-ALOHA (with and without code sharing) and TDMA-ALOHA; we also consider carrier sensing and collision detection versions of these protocols. In each case, saturation throughput can be obtained via analysis pf a continuous time Markov chain. Our results show how saturation throughput degrades with code-sharing. Finally, we also present some simulation results for mean packet delay. Our work is motivated by optical CDMA in which "chips" can be optically generated, and hence the achievable chip rate can exceed the achievable TDMA bit rate which is limited by electronics. Code sharing may be useful in the optical CDMA context as it reduces the number of optical correlators at the receivers. Our throughput results help to quantify by how much the CDMA chip rate should exceed the TDMA bit rate so that CDMA-ALOHA yields better capacity than TDMA-ALOHA.

Rainbow Connection Number of Graph Power and Graph Products

Rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same (note that the coloring need not be proper). In this paper we study the rainbow connection number with respect to three important graph product operations (namely the Cartesian product, the lexicographic product and the strong product) and the operation of taking the power of a graph. In this direction, we show that if G is a graph obtained by applying any of the operations mentioned above on non-trivial graphs, then rc(G) a parts per thousand currency sign 2r(G) + c, where r(G) denotes the radius of G and . In general the rainbow connection number of a bridgeless graph can be as high as the square of its radius 1]. This is an attempt to identify some graph classes which have rainbow connection number very close to the obvious lower bound of diameter (and thus the radius). The bounds reported are tight up to additive constants. The proofs are constructive and hence yield polynomial time -factor approximation algorithms.

On the Maximum Number of Linearly Independent Cycles and Paths in a Network

Central to network tomography is the problem of identifiability, the ability to identify internal network characteristics uniquely from end-to-end measurements. This problem is often underconstrained even when internal network characteristics such as link delays are modeled as additive constants. While it is known that the network topology can play a role in determining the extent of identifiability, there is a lack in the fundamental understanding of being able to quantify it for a given network. In this paper, we consider the problem of identifying additive link metrics in an arbitrary undirected network using measurement nodes and establishing paths/cycles between them. For a given placement of measurement nodes, we define and derive the ``link rank'' of the network-the maximum number of linearly independent cycles/paths that may be established between the measurement nodes. We achieve this in linear time. The link rank helps quantify the exact extent of identifiability in a network. We also develop a quadratic time algorithm to compute a set of cycles/paths that achieves the maximum rank.

Mode coupling theory analysis of electrolyte solutions: Time dependent diffusion, intermediate scattering function, and ion solvation dynamics

A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) intermediate scattering function of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics with implicit water molecules and molecular dynamics method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding intermediate scattering function evaluated from our MCT approach show quantitative agreement with early experimental and present Brownian dynamic simulation results. With increasing concentration, the dispersion of electrolyte friction is found to occur at increasingly higher frequency, due to the faster relaxation of the ion atmosphere. The wave number dependence of intermediate scattering function, F(k, t), exhibits markedly different relaxation dynamics at different length scales. At small wave numbers, we find the emergence of a step-like relaxation, indicating the presence of both fast and slow time scales in the system. Such behavior allows an intriguing analogy with temperature dependent relaxation dynamics of supercooled liquids. We find that solvation dynamics of a tagged ion exhibits a power law decay at long times-the decay can also be fitted to a stretched exponential form. The emergence of the power law in solvation dynamics has been tested by carrying out long Brownian dynamics simulations with varying ionic concentrations. The solvation time correlation and ion-ion intermediate scattering function indeed exhibit highly interesting, non-trivial dynamical behavior at intermediate to longer times that require further experimental and theoretical studies. (c) 2015 AIP Publishing LLC.

On the number of two-line and three-line latin rectangles - an alternative approach

The number of two-line and three-line Latin rectangles is obtained by recursive methods in a setting slightly more general than usually considered. We show how this leads to a generalisation which is proved elsewhere.

Invariance group properties and exact solutions of equations describing time-dependent free surface flows under gravity

Using the method of infinitesimal transformations, a 6-parameter family of exact solutions describing nonlinear sheared flows with a free surface are found. These solutions are a hybrid between the earlier self-propagating simple wave solutions of Freeman, and decaying solutions of Sachdev. Simple wave solutions are also derived via the method of infinitesimal transformations. Incomplete beta functions seem to characterize these (nonlinear) sheared flows in the absence of critical levels.

On various types of decoupling for time-varying system

This paper deals with the problem of decoupling a class of linear time-varying multi-variable systems, based on the defining property that the impulse response matrix of a decoupled system is diagonal. Depending on the properties of the coefficient matrices of the vector differential equation of the open-loop system, the system may be uniformly or totally decoupled. The necessary and sufficient conditions that permit a system to be uniformly or totally decoupled by state variable feedback are given. The main contribution of this paper is the precise definition of these two classes of decoupling and a rigorous derivation of the necessary and sufficient conditions which show the necessity of requiring that the system be of constant ordered rank with respect to observability. A simple example illustrates the importance of having several definitions of decoupling. Finally, the results are specialized to the case of time invariant systems.

A differential transformation technique for the analysis of a class of non-linear time varying systems

The scope of the differential transformation technique, developed earlier for the study of non-linear, time invariant systems, has been extended to the domain of time-varying systems by modifications to the differential transformation laws proposed therein. Equivalence of a class of second-order, non-linear, non-autonomous systems with a linear autonomous model of second order is established through these transformation laws. The feasibility of application of this technique in obtaining the response of such non-linear time-varying systems is discussed.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

A note on the Hadwiger number of circular arc graphs

The intention of this note is to motivate the researchers to study Hadwiger's conjecture for circular arc graphs. Let η(G) denote the largest clique minor of a graph G, and let χ(G) denote its chromatic number. Hadwiger's conjecture states that η(G)greater-or-equal, slantedχ(G) and is one of the most important and difficult open problems in graph theory. From the point of view of researchers who are sceptical of the validity of the conjecture, it is interesting to study the conjecture for graph classes where η(G) is guaranteed not to grow too fast with respect to χ(G), since such classes of graphs are indeed a reasonable place to look for possible counterexamples. We show that in any circular arc graph G, η(G)less-than-or-equals, slant2χ(G)−1, and there is a family with equality. So, it makes sense to study Hadwiger's conjecture for this family.