Liouville's theorem and power series for quaternionic functions

In recent years quaternionic functions have been an intense and prosperous object of research, and important results were determined [1]-[6]. Some of these results are similar to well known cases in one complex variable, op. cit. [5], [6]. In this paper the hypercomplex expansion of a function in a power series as well as determination of a Liouville's type theorem have been investigated to the quaternionic functions. In this case, it is observed that the Liouville's type theorem is true for second order derivatives, which differs from its classical version. © 2011 Academic Publications, Ltd.

Pricing of reactive power support provided by distributed generators in transmission systems

Distributed Generation, microgrid technologies, two-way communication systems, and demand response programs are issues that are being studied in recent years within the concept of smart grids. At some level of enough penetration, the Distributed Generators (DGs) can provide benefits for sub-transmission and transmission systems through the so-called ancillary services. This work is focused on the ancillary service of reactive power support provided by DGs, specifically Wind Turbine Generators (WTGs), with high level of impact on transmission systems. The main objective of this work is to propose an optimization methodology to price this service by determining the costs in which a DG incurs when it loses sales opportunity of active power, i.e, by determining the Loss of Opportunity Costs (LOC). LOC occur when more reactive power is required than available, and the active power generation has to be reduced in order to increase the reactive power capacity. In the optimization process, three objectives are considered: active power generation costs of DGs, voltage stability margin of the system, and losses in the lines of the network. Uncertainties of WTGs are reduced solving multi-objective optimal power flows in multiple probabilistic scenarios constructed by Monte Carlo simulations, and modeling the time series associated with the active power generation of each WTG via Fuzzy Logic and Markov Chains. The proposed methodology was tested using the IEEE 14 bus test system with two WTGs installed. © 2011 IEEE.

Advancing the Goals of the 2005 UNESCO Convention on the Diversity of Cultural Expressions in the Fields of Education, Participation of Civil Society and Sustainable Development

This is a contribution to an expert opinion to be submitted to Intergovernmental Committee of the UNESCO Convention on Cultural Diversity. It seeks to identify recommendations for action in the fields of education, participation of the civil society and sustainable development (under respectively Articles 10, 11 and 13 of the Convention), which are to be specifically targeted taking into account the changed and changing conditions of the digital networked environment.

A dynamic factor model for mid-term forecasting of wind power generation

The main objective of this paper is the development and application of multivariate time series models for forecasting aggregated wind power production in a country or region. Nowadays, in Spain, Denmark or Germany there is an increasing penetration of this kind of renewable energy, somehow to reduce energy dependence on the exterior, but always linked with the increaseand uncertainty affecting the prices of fossil fuels. The disposal of accurate predictions of wind power generation is a crucial task both for the System Operator as well as for all the agents of the Market. However, the vast majority of works rarely onsider forecasting horizons longer than 48 hours, although they are of interest for the system planning and operation. In this paper we use Dynamic Factor Analysis, adapting and modifying it conveniently, to reach our aim: the computation of accurate forecasts for the aggregated wind power production in a country for a forecasting horizon as long as possible, particularly up to 60 days (2 months). We illustrate this methodology and the results obtained for real data in the leading country in wind power production: Denmark

Numerical modeling of electromagnetic coupling phenomena in the vicinities of overhead power transmission lines.

Electromagnetic coupling phenomena between overhead power transmission lines and other nearby structures are inevitable, especially in densely populated areas. The undesired effects resulting from this proximity are manifold and range from the establishment of hazardous potentials to the outbreak of alternate current corrosion phenomena. The study of this class of problems is necessary for ensuring security in the vicinities of the interaction zone and also to preserve the integrity of the equipment and of the devices there present. However, the complete modeling of this type of application requires the three- -dimensional representation of the region of interest and needs specific numerical methods for field computation. In this work, the modeling of problems arising from the flow of electrical currents in the ground (the so-called conductive coupling) will be addressed with the finite element method. Those resulting from the time variation of the electromagnetic fields (the so-called inductive coupling) will be considered as well, and they will be treated with the generalized PEEC (Partial Element Equivalent Circuit) method. More specifically, a special boundary condition on the electric potential is proposed for truncating the computational domain in the finite element analysis of conductive coupling problems, and a complete PEEC formulation for modeling inductive coupling problems is presented. Test configurations of increasing complexities are considered for validating the foregoing approaches. These works aim to provide a contribution to the modeling of this class of problems, which tend to become common with the expansion of power grids.

THE DESIGN OF A POWER SYSTEM FOR A WIRELESS SENSOR NETWORK FOR LONG-TERM OPERATION

Wireless sensor networks (WSNs) have shown wide applicability to many fields including monitoring of environmental, civil, and industrial settings. WSNs however are resource constrained by many competing factors that span their hardware, software, and networking. One of the central resource constrains is the charge consumption of WSN nodes. With finite energy supplies, low charge consumption is needed to ensure long lifetimes and success of WSNs. This thesis details the design of a power system to support long-term operation of WSNs. The power system’s development occurs in parallel with a custom WSN from the Queen’s MEMS Lab (QML-WSN), with the goal of supporting a 1+ year lifetime without sacrificing functionality. The final power system design utilizes a TPS62740 DC-DC converter with AA alkaline batteries to efficiently supply the nodes while providing battery monitoring functionality and an expansion slot for future development. Testing tools for measuring current draw and charge consumption were created along with analysis and processing software. Through their use charge consumption of the power system was drastically lowered and issues in QML-WSN were identified and resolved including the proper shutdown of accelerometers, and incorrect microcontroller unit (MCU) power pin connection. Controlled current profiling revealed unexpected behaviour of nodes and detailed current-voltage relationships. These relationships were utilized with a lifetime projection model to estimate a lifetime between 521-551 days, depending on the mode of operation. The power system and QML-WSN were tested over a long term trial lasting 272+ days in an industrial testbed to monitor an air compressor pump. Environmental factors were found to influence the behaviour of nodes leading to increased charge consumption, while a node in an office setting was still operating at the conclusion of the trail. This agrees with the lifetime projection and gives a strong indication that a 1+ year lifetime is achievable. Additionally, a light-weight charge consumption model was developed which allows charge consumption information of nodes in a distributed WSN to be monitored. This model was tested in a laboratory setting demonstrating +95% accuracy for high packet reception rate WSNs across varying data rates, battery supply capacities, and runtimes up to full battery depletion.

The fundamentals of air power, an address; with introductory remarks by John Dwight Sullivan.

"Selected references on air power prepared by Aeronautics Division, the Library of Congress": p. 22-23.

Formal group laws and hypergraph colorings

Thesis (Ph.D.)--University of Washington, 2016-06

Visualization of Cerenkov radiation and the fields of a moving charge

For some physics students, the concept of a particle travelling faster than the speed of light holds endless fascination, and. Cerenkov radiation is a visible consequence of a charged particle travelling through a medium at locally superluminal velocities. The Heaviside-Feynman equations for calculating the magnetic and electric fields of a moving charge have been known for many decades, but it is only recently that the computing power to plot the fields of such a particle has become readily available for student use. This paper investigates and illustrates the calculation of Maxwell's D field in homogeneous isotropic media for arbitrary, including superluminal, constant velocity, and uses the results as a basis for discussing energy transfer in the electromagnetic field.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20

THE DESIGN OF A POWER SYSTEM FOR A WIRELESS SENSOR NETWORK FOR LONG-TERM OPERATION

Wireless sensor networks (WSNs) have shown wide applicability to many fields including monitoring of environmental, civil, and industrial settings. WSNs however are resource constrained by many competing factors that span their hardware, software, and networking. One of the central resource constrains is the charge consumption of WSN nodes. With finite energy supplies, low charge consumption is needed to ensure long lifetimes and success of WSNs. This thesis details the design of a power system to support long-term operation of WSNs. The power system’s development occurs in parallel with a custom WSN from the Queen’s MEMS Lab (QML-WSN), with the goal of supporting a 1+ year lifetime without sacrificing functionality. The final power system design utilizes a TPS62740 DC-DC converter with AA alkaline batteries to efficiently supply the nodes while providing battery monitoring functionality and an expansion slot for future development. Testing tools for measuring current draw and charge consumption were created along with analysis and processing software. Through their use charge consumption of the power system was drastically lowered and issues in QML-WSN were identified and resolved including the proper shutdown of accelerometers, and incorrect microcontroller unit (MCU) power pin connection. Controlled current profiling revealed unexpected behaviour of nodes and detailed current-voltage relationships. These relationships were utilized with a lifetime projection model to estimate a lifetime between 521-551 days, depending on the mode of operation. The power system and QML-WSN were tested over a long term trial lasting 272+ days in an industrial testbed to monitor an air compressor pump. Environmental factors were found to influence the behaviour of nodes leading to increased charge consumption, while a node in an office setting was still operating at the conclusion of the trail. This agrees with the lifetime projection and gives a strong indication that a 1+ year lifetime is achievable. Additionally, a light-weight charge consumption model was developed which allows charge consumption information of nodes in a distributed WSN to be monitored. This model was tested in a laboratory setting demonstrating +95% accuracy for high packet reception rate WSNs across varying data rates, battery supply capacities, and runtimes up to full battery depletion.

An Analysis of Colombian Power Market Price Behavior from an Industrial Organization Perspective

We analyze the behavior of spot prices in the Colombian wholesale power market, using a series of models derived from industrial organization theory -- We first create a Cournot-based model that simulates the strategic behavior of the market-leader power generators, which we use to estimate two industrial organization variables, the Index of Residual Demand and the Herfindahl-Hirschman Index (HHI) -- We use these variables to create VAR models that estimate spot prices and power market impulse-response relationships -- The results from these models show that hydroelectric generators can use their water storage capability strategically to affect off-peak prices primarily, while the thermal generators can manage their capacity strategically to affect on-peak prices -- In addition, shocks to the Index of Residual Capacity and to the HHI cause spot price fluctuations, which can be interpreted as the generators´ strategic response to these shocks