On the Wave Propagation of Disturbances in Homogeneous Electromechanical Systems

In this paper, we make an attempt to describe the phenomenon of wave propagation when a disturbance is introduced in an electromechanical system having a lumped parameter representation. We initially discuss mechanical waves in homogeneous spring mass systems and then focus on electromechanical wave propagation in power systems. We primarily discuss ring and open end systems. Eigenvalue analysis of the system is done to find the behavior of the orthogonal modes as a function of time and space. We then derive an expression for velocity of propagation of the disturbance wave and the transport delay associated with it. Effects of system parameters, like generator inertia and transmission line resistance, are also discussed. Although the theory was developed considering homogeneous systems (identical values of inertia/mass, line parameters/spring constant, etc.), an implementation on a nonhomogeneous system is also presented in this paper. Numerical simulations were done and compared with the analytical results derived in this paper.

Representation of a Solution of the Cauchy Problem for an Oscillating System with Multiple Delays and Pairwise Permutable Matrices

Nonhomogeneous system of linear differential equations of second order with multiple different delays and pairwise permutable matrices defining the linear parts is considered. Solution of corresponding initial value problem is represented using matrix polynomials.

Weyl-Titchmarsh Theory for Time Scale Symplectic Systems on Half Line

We develop the Weyl-Titchmarsh theory for time scale symplectic systems. We introduce theM(λ)-function, study its properties, construct the corresponding Weyl disk and Weyl circle, and establish their geometric structure including the formulas for their center and matrix radii. Similar properties are then derived for the limiting Weyl disk. We discuss the notions of the system being in the limit point or limit circle case and prove several characterizations of the system in the limit point case and one condition for the limit circle case. We also define the Green function for the associated nonhomogeneous system and use its properties for deriving further results for the original system in the limit point or limit circle case. Our work directly generalizes the corresponding discrete time theory obtained recently by S. Clark and P. Zemánek (2010). It also unifies the results in many other papers on the Weyl-Titchmarsh theory for linear Hamiltonian differential, difference, and dynamic systems when the spectral parameter appears in the second equation. Some of our results are new even in the case of the second-order Sturm-Liouville equations on time scales.

A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution

In this work, a class of multidimensional stochastic hybrid dynamic models is studied. The system under investigation is a first-order linear nonhomogeneous system of Itô-Doob type stochastic differential equations with switching coefficients. The switching of the system is governed by a discrete dynamic which is monitored by a non-homogeneous Poisson process. Closed-form solutions of the systems are obtained. Furthermore, the major part of the work is devoted to finding closed-form probability density functions of the solution processes of linear homogeneous and Ornstein-Uhlenbeck type systems with jumps.

DYNAMIC VISIT-ORDER RULES FOR BATCH-SERVICE POLLING

We explore visit-order policies in nonsymmetric polling systems with switch-in and switch-out times, where service is in batches of unlimited size. We concentrate on so-called “Hamiltonian tour” policies in which, in order to give a fair treatment to the various users, the server attends every nonempty queue exactly once during each round of visits (cycle). The server dynamically generates a new visit schedule at the start of each round, depending on the current state of the system (number of jobs in each queue) and on the various nonhomogeneous system parameters. We consider three service regimes, globally gated, (locally) gated, and exhaustive, and study three different performance measures: (1) minimizing the expected weighted sum of all sojourn times of jobs within a cycle; (2) minimizing the expected length of the next cycle, and (3) maximizing the expected weighted throughput in a cycle. For each combination of performance measure and service regime, we derive characteristics of the optimal Hamiltonian tour. Some of the resulting optimal policies are shown to be elegant index-type rules. Others are the solutions of deterministic NP-hard problems. Special cases are reduced to assignment problems with specific cost matrices. The index-type rules can further be used to construct fixed-order, cyclic-type polling tables in cases where dynamic control is not applicable.