Electric current of an electrified jet issuing from a long metallic tube.

This paper presents an analysis of the transport of electric current in a jet of an electrically conducting liquid discharging from a metallic tube into a gas or a vacuum, and subject to an electric field due to a high voltage applied between the tube and a far electrode. The flow, the surface charge and the electric field are computed in the current transfer region of the jet, where conduction current in the liquid becomes surface current due to the convection of electric charge accumulated at its surface. The electric current computed as a function of the flow rate of the liquid injected through the tube increases first as the square root of this flow rate, levels to a nearly constant value when the flow rate is increased and finally sets to a linear increase when the flow rate is further increased. The current increases linearly with the applied voltage at small and moderate values of this variable, and faster than linearly at high voltages. The characteristic length and structure of the current transfer region are determined. Order-of-magnitude estimates for jets which are only weakly stretched by the electric stresses are worked out that qualitatively account for some of the numerical results.

Co-simulation Methodologies for Hybrid and Electric Vehicle Dynamics

In recent decades, full electric and hybrid electric vehicles have emerged as an alternative to conventional cars due to a range of factors, including environmental and economic aspects. These vehicles are the result of considerable efforts to seek ways of reducing the use of fossil fuel for vehicle propulsion. Sophisticated technologies such as hybrid and electric powertrains require careful study and optimization. Mathematical models play a key role at this point. Currently, many advanced mathematical analysis tools, as well as computer applications have been built for vehicle simulation purposes. Given the great interest of hybrid and electric powertrains, along with the increasing importance of reliable computer-based models, the author decided to integrate both aspects in the research purpose of this work. Furthermore, this is one of the first final degree projects held at the ETSII (Higher Technical School of Industrial Engineers) that covers the study of hybrid and electric propulsion systems. The present project is based on MBS3D 2.0, a specialized software for the dynamic simulation of multibody systems developed at the UPM Institute of Automobile Research (INSIA). Automobiles are a clear example of complex multibody systems, which are present in nearly every field of engineering. The work presented here benefits from the availability of MBS3D software. This program has proven to be a very efficient tool, with a highly developed underlying mathematical formulation. On this basis, the focus of this project is the extension of MBS3D features in order to be able to perform dynamic simulations of hybrid and electric vehicle models. This requires the joint simulation of the mechanical model of the vehicle, together with the model of the hybrid or electric powertrain. These sub-models belong to completely different physical domains. In fact the powertrain consists of energy storage systems, electrical machines and power electronics, connected to purely mechanical components (wheels, suspension, transmission, clutch…). The challenge today is to create a global vehicle model that is valid for computer simulation. Therefore, the main goal of this project is to apply co-simulation methodologies to a comprehensive model of an electric vehicle, where sub-models from different areas of engineering are coupled. The created electric vehicle (EV) model consists of a separately excited DC electric motor, a Li-ion battery pack, a DC/DC chopper converter and a multibody vehicle model. Co-simulation techniques allow car designers to simulate complex vehicle architectures and behaviors, which are usually difficult to implement in a real environment due to safety and/or economic reasons. In addition, multi-domain computational models help to detect the effects of different driving patterns and parameters and improve the models in a fast and effective way. Automotive designers can greatly benefit from a multidisciplinary approach of new hybrid and electric vehicles. In this case, the global electric vehicle model includes an electrical subsystem and a mechanical subsystem. The electrical subsystem consists of three basic components: electric motor, battery pack and power converter. A modular representation is used for building the dynamic model of the vehicle drivetrain. This means that every component of the drivetrain (submodule) is modeled separately and has its own general dynamic model, with clearly defined inputs and outputs. Then, all the particular submodules are assembled according to the drivetrain configuration and, in this way, the power flow across the components is completely determined. Dynamic models of electrical components are often based on equivalent circuits, where Kirchhoff’s voltage and current laws are applied to draw the algebraic and differential equations. Here, Randles circuit is used for dynamic modeling of the battery and the electric motor is modeled through the analysis of the equivalent circuit of a separately excited DC motor, where the power converter is included. The mechanical subsystem is defined by MBS3D equations. These equations consider the position, velocity and acceleration of all the bodies comprising the vehicle multibody system. MBS3D 2.0 is entirely written in MATLAB and the structure of the program has been thoroughly studied and understood by the author. MBS3D software is adapted according to the requirements of the applied co-simulation method. Some of the core functions are modified, such as integrator and graphics, and several auxiliary functions are added in order to compute the mathematical model of the electrical components. By coupling and co-simulating both subsystems, it is possible to evaluate the dynamic interaction among all the components of the drivetrain. ‘Tight-coupling’ method is used to cosimulate the sub-models. This approach integrates all subsystems simultaneously and the results of the integration are exchanged by function-call. This means that the integration is done jointly for the mechanical and the electrical subsystem, under a single integrator and then, the speed of integration is determined by the slower subsystem. Simulations are then used to show the performance of the developed EV model. However, this project focuses more on the validation of the computational and mathematical tool for electric and hybrid vehicle simulation. For this purpose, a detailed study and comparison of different integrators within the MATLAB environment is done. Consequently, the main efforts are directed towards the implementation of co-simulation techniques in MBS3D software. In this regard, it is not intended to create an extremely precise EV model in terms of real vehicle performance, although an acceptable level of accuracy is achieved. The gap between the EV model and the real system is filled, in a way, by introducing the gas and brake pedals input, which reflects the actual driver behavior. This input is included directly in the differential equations of the model, and determines the amount of current provided to the electric motor. For a separately excited DC motor, the rotor current is proportional to the traction torque delivered to the car wheels. Therefore, as it occurs in the case of real vehicle models, the propulsion torque in the mathematical model is controlled through acceleration and brake pedal commands. The designed transmission system also includes a reduction gear that adapts the torque coming for the motor drive and transfers it. The main contribution of this project is, therefore, the implementation of a new calculation path for the wheel torques, based on performance characteristics and outputs of the electric powertrain model. Originally, the wheel traction and braking torques were input to MBS3D through a vector directly computed by the user in a MATLAB script. Now, they are calculated as a function of the motor current which, in turn, depends on the current provided by the battery pack across the DC/DC chopper converter. The motor and battery currents and voltages are the solutions of the electrical ODE (Ordinary Differential Equation) system coupled to the multibody system. Simultaneously, the outputs of MBS3D model are the position, velocity and acceleration of the vehicle at all times. The motor shaft speed is computed from the output vehicle speed considering the wheel radius, the gear reduction ratio and the transmission efficiency. This motor shaft speed, somehow available from MBS3D model, is then introduced in the differential equations corresponding to the electrical subsystem. In this way, MBS3D and the electrical powertrain model are interconnected and both subsystems exchange values resulting as expected with tight-coupling approach.When programming mathematical models of complex systems, code optimization is a key step in the process. A way to improve the overall performance of the integration, making use of C/C++ as an alternative programming language, is described and implemented. Although this entails a higher computational burden, it leads to important advantages regarding cosimulation speed and stability. In order to do this, it is necessary to integrate MATLAB with another integrated development environment (IDE), where C/C++ code can be generated and executed. In this project, C/C++ files are programmed in Microsoft Visual Studio and the interface between both IDEs is created by building C/C++ MEX file functions. These programs contain functions or subroutines that can be dynamically linked and executed from MATLAB. This process achieves reductions in simulation time up to two orders of magnitude. The tests performed with different integrators, also reveal the stiff character of the differential equations corresponding to the electrical subsystem, and allow the improvement of the cosimulation process. When varying the parameters of the integration and/or the initial conditions of the problem, the solutions of the system of equations show better dynamic response and stability, depending on the integrator used. Several integrators, with variable and non-variable step-size, and for stiff and non-stiff problems are applied to the coupled ODE system. Then, the results are analyzed, compared and discussed. From all the above, the project can be divided into four main parts: 1. Creation of the equation-based electric vehicle model; 2. Programming, simulation and adjustment of the electric vehicle model; 3. Application of co-simulation methodologies to MBS3D and the electric powertrain subsystem; and 4. Code optimization and study of different integrators. Additionally, in order to deeply understand the context of the project, the first chapters include an introduction to basic vehicle dynamics, current classification of hybrid and electric vehicles and an explanation of the involved technologies such as brake energy regeneration, electric and non-electric propulsion systems for EVs and HEVs (hybrid electric vehicles) and their control strategies. Later, the problem of dynamic modeling of hybrid and electric vehicles is discussed. The integrated development environment and the simulation tool are also briefly described. The core chapters include an explanation of the major co-simulation methodologies and how they have been programmed and applied to the electric powertrain model together with the multibody system dynamic model. Finally, the last chapters summarize the main results and conclusions of the project and propose further research topics. In conclusion, co-simulation methodologies are applicable within the integrated development environments MATLAB and Visual Studio, and the simulation tool MBS3D 2.0, where equation-based models of multidisciplinary subsystems, consisting of mechanical and electrical components, are coupled and integrated in a very efficient way.

Código híbrido avanzado de motores de plasma de efecto Hall

La propulsión eléctrica constituye hoy una tecnología muy competitiva y de gran proyección de futuro. Dentro de los diversos motores de plasma existentes, el motor de efecto Hall ha adquirido una gran madurez y constituye un medio de propulsión idóneo para un rango amplio de misiones. En la presente Tesis se estudian los motores Hall con geometría convencional y paredes dieléctricas. La compleja interacción entre los múltiples fenómenos físicos presentes hace que sea difícil la simulación del plasma en estos motores. Los modelos híbridos son los que representan un mejor compromiso entre precisión y tiempo de cálculo. Se basan en utilizar un modelo fluido para los electrones y algoritmos de dinámica de partículas PIC (Particle-In- Cell) para los iones y los neutros. Permiten hacer uso de la hipótesis de cuasineutralidad del plasma, a cambio de resolver separadamente las capas límite (o vainas) que se forman en torno a las paredes de la cámara. Partiendo de un código híbrido existente, llamado HPHall-2, el objetivo de la Tesis doctoral ha sido el desarrollo de un código híbrido avanzado que mejorara la simulación de la descarga de plasma en un motor de efecto Hall. Las actualizaciones y mejoras realizadas en las diferentes partes que componen el código comprenden tanto aspectos teóricos como numéricos. Fruto de la extensa revisión de la algoritmia del código HPHall-2 se han conseguido reducir los errores de precisión un orden de magnitud, y se ha incrementado notablemente su consistencia y robustez, permitiendo la simulación del motor en un amplio rango de condiciones. Algunos aspectos relevantes a destacar en el subcódigo de partículas son: la implementación de un nuevo algoritmo de pesado que permite determinar de forma más precisa el flujo de las magnitudes del plasma; la implementación de un nuevo algoritmo de control de población, que permite tener suficiente número de partículas cerca de las paredes de la cámara, donde los gradientes son mayores y las condiciones de cálculo son más críticas; las mejoras en los balances de masa y energía; y un mejor cálculo del campo eléctrico en una malla no uniforme. Merece especial atención el cumplimiento de la condición de Bohm en el borde de vaina, que en los códigos híbridos representa una condición de contorno necesaria para obtener una solución consistente con el modelo de interacción plasma-pared, y que en HPHall-2 aún no se había resuelto satisfactoriamente. En esta Tesis se ha implementado el criterio cinético de Bohm para una población de iones con diferentes cargas eléctricas y una gran dispersión de velocidades. En el código, el cumplimiento de la condición cinética de Bohm se consigue por medio de un algoritmo que introduce una fina capa de aceleración nocolisional adyacente a la vaina y mide adecuadamente el flujo de partículas en el espacio y en el tiempo. Las mejoras realizadas en el subcódigo de electrones incrementan la capacidad de simulación del código, especialmente en la región aguas abajo del motor, donde se simula la neutralización del chorro del plasma por medio de un modelo de cátodo volumétrico. Sin abordar el estudio detallado de la turbulencia del plasma, se implementan modelos sencillos de ajuste de la difusión anómala de Bohm, que permiten reproducir los valores experimentales del potencial y la temperatura del plasma, así como la corriente de descarga del motor. En cuanto a los aspectos teóricos, se hace especial énfasis en la interacción plasma-pared y en la dinámica de los electrones secundarios libres en el interior del plasma, cuestiones que representan hoy en día problemas abiertos en la simulación de los motores Hall. Los nuevos modelos desarrollados buscan una imagen más fiel a la realidad. Así, se implementa el modelo de vaina de termalización parcial, que considera una función de distribución no-Maxwelliana para los electrones primarios y contabiliza unas pérdidas energéticas más cercanas a la realidad. Respecto a los electrones secundarios, se realiza un estudio cinético simplificado para evaluar su grado de confinamiento en el plasma, y mediante un modelo fluido en el límite no-colisional, se determinan las densidades y energías de los electrones secundarios libres, así como su posible efecto en la ionización. El resultado obtenido muestra que los electrones secundarios se pierden en las paredes rápidamente, por lo que su efecto en el plasma es despreciable, no así en las vainas, donde determinan el salto de potencial. Por último, el trabajo teórico y de simulación numérica se complementa con el trabajo experimental realizado en el Pnnceton Plasma Physics Laboratory, en el que se analiza el interesante transitorio inicial que experimenta el motor en el proceso de arranque. Del estudio se extrae que la presencia de gases residuales adheridos a las paredes juegan un papel relevante, y se recomienda, en general, la purga completa del motor antes del modo normal de operación. El resultado final de la investigación muestra que el código híbrido desarrollado representa una buena herramienta de simulación de un motor Hall. Reproduce adecuadamente la física del motor, proporcionando resultados similares a los experimentales, y demuestra ser un buen laboratorio numérico para estudiar el plasma en el interior del motor. Abstract Electric propulsion is today a very competitive technology and has a great projection into the future. Among the various existing plasma thrusters, the Hall effect thruster has acquired a considerable maturity and constitutes an ideal means of propulsion for a wide range of missions. In the present Thesis only Hall thrusters with conventional geometry and dielectric walls are studied. The complex interaction between multiple physical phenomena makes difficult the plasma simulation in these engines. Hybrid models are those representing a better compromise between precision and computational cost. They use a fluid model for electrons and Particle-In-Cell (PIC) algorithms for ions and neutrals. The hypothesis of plasma quasineutrality is invoked, which requires to solve separately the sheaths formed around the chamber walls. On the basis of an existing hybrid code, called HPHall-2, the aim of this doctoral Thesis is to develop an advanced hybrid code that better simulates the plasma discharge in a Hall effect thruster. Updates and improvements of the code include both theoretical and numerical issues. The extensive revision of the algorithms has succeeded in reducing the accuracy errors in one order of magnitude, and the consistency and robustness of the code have been notably increased, allowing the simulation of the thruster in a wide range of conditions. The most relevant achievements related to the particle subcode are: the implementation of a new weighing algorithm that determines more accurately the plasma flux magnitudes; the implementation of a new algorithm to control the particle population, assuring enough number of particles near the chamber walls, where there are strong gradients and the conditions to perform good computations are more critical; improvements in the mass and energy balances; and a new algorithm to compute the electric field in a non-uniform mesh. It deserves special attention the fulfilment of the Bohm condition at the edge of the sheath, which represents a boundary condition necessary to match consistently the hybrid code solution with the plasma-wall interaction, and remained as a question unsatisfactory solved in the HPHall-2 code. In this Thesis, the kinetic Bohm criterion has been implemented for an ion particle population with different electric charges and a large dispersion in their velocities. In the code, the fulfilment of the kinetic Bohm condition is accomplished by an algorithm that introduces a thin non-collisional layer next to the sheaths, producing the ion acceleration, and measures properly the flux of particles in time and space. The improvements made in the electron subcode increase the code simulation capabilities, specially in the region downstream of the thruster, where the neutralization of the plasma jet is simulated using a volumetric cathode model. Without addressing the detailed study of the plasma turbulence, simple models for a parametric adjustment of the anomalous Bohm difussion are implemented in the code. They allow to reproduce the experimental values of the plasma potential and the electron temperature, as well as the discharge current of the thruster. Regarding the theoretical issues, special emphasis has been made in the plasma-wall interaction of the thruster and in the dynamics of free secondary electrons within the plasma, questions that still remain unsolved in the simulation of Hall thrusters. The new developed models look for results closer to reality, such as the partial thermalization sheath model, that assumes a non-Maxwellian distribution functions for primary electrons, and better computes the energy losses at the walls. The evaluation of secondary electrons confinement within the chamber is addressed by a simplified kinetic study; and using a collisionless fluid model, the densities and energies of free secondary electrons are computed, as well as their effect on the plasma ionization. Simulations show that secondary electrons are quickly lost at walls, with a negligible effect in the bulk of the plasma, but they determine the potential fall at sheaths. Finally, numerical simulation and theoretical work is complemented by the experimental work carried out at the Princeton Plasma Physics Laboratory, devoted to analyze the interesting transitional regime experienced by the thruster in the startup process. It is concluded that the gas impurities adhered to the thruster walls play a relevant role in the transitional regime and, as a general recomendation, a complete purge of the thruster before starting its normal mode of operation it is suggested. The final result of the research conducted in this Thesis shows that the developed code represents a good tool for the simulation of Hall thrusters. The code reproduces properly the physics of the thruster, with results similar to the experimental ones, and represents a good numerical laboratory to study the plasma inside the thruster.

Impacto del vehículo eléctrico sobre las redes de distribución

Es objeto del presente proyecto definir red inteligente (Smart Grid) como parte fundamental de un futuro sistema de generación, distribución y transporte de la energía, utilizando como medio principal de desplazamiento el Vehículo Eléctrico. El desarrollo del proyecto se lleva a cabo a través de un análisis exhaustivo del impacto de la introducción masiva del Vehículo Eléctrico en las redes de distribución. Para evaluar las simulaciones se han creado unos niveles de penetración de vehículos, así como el despliegue de dispositivos de recarga y hora óptima de conexión a la red para que la curva de demanda se suavice lo máximo posible y las infraestructuras eléctricas no sufran una sobrecarga provocando una caída del sistema eléctrico. Con un software específico, se ha obtenido un porcentaje de pérdidas y se han sacado unas conclusiones para los distintos casos de penetración del vehículo eléctrico. Asimismo, se ha analizado la implementación de un sistema que estudie los intercambios energéticos que se producen entre los diferentes sistemas del vehículo, y entre éste y su entorno para poder disminuir las pérdidas. ABSTRACT The objective of this project is to define Smart Grid as an essential part of a future generation system, distribution and transmission of energy, using Electric Vehicle as primary mean of moving. The development of this project was carried out through a comprehensive analysis of the impact of the massive introduction of electric vehicles in distribution networks. To evaluate the simulations, different indicators for vehicle´s penetration were created, as well as the deployment of charging devices and optimal time to get network connection in order to smooth the demand curve as much as possible and to avoid electrical infrastructure being overloaded and thus causing the electrical system to stop working. For each of the different cases of electric vehicles’ penetration a percentage of losses and conclusions were drawn using specific software. The implementation of a system that studies the exchanges of energy that occur between different vehicle systems and between itself and its environment to reduce losses was also analyzed.

Perfect imaging analysis of the spherical geodesic waveguide

Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electromagnetic fields, emitted by an object plane, towards an image plane producing the same field distribution in both planes. In particular, a Dirac delta electric field in the object plane is focused without diffraction limit to the Dirac delta electric field in the image plane. Two devices with positive refraction, the Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Although these systems can detect displacements up to ?/3000, they cannot be compared to the NRL, since the concept of image is different. The SGW deals only with point source and drain, while in the case of the NRL, there is an object and an image surface. Here, it is presented an analysis of the SGW with defined object and image surfaces (both are conical surfaces), similarly as in the case of the NRL. The results show that a Dirac delta electric field on the object surface produces an image below the diffraction limit on the image surface.

Integración de baterías en sistemas fotovoltaicos conectados a red

La situación actual del mercado energético en España y el imparable aumento de las tasas por parte de las eléctricas, está fomentando la búsqueda de fuentes de energía alternativas que permitan a la población poder abastecerse de electricidad, sin tener que pagar unos costes tan elevados. Para cubrir esta necesidad, la energía fotovoltaica y sobretodo el autoconsumo con inyección a red o balance neto, está adquiriendo cada vez más importancia dentro del mundo energético. Pero la penetración de esta tecnología en la Red Eléctrica Española tiene un freno, la desconfianza por parte del operador de la red, ya que la fotovoltaica es una fuente de energía intermitente, que puede introducir inestabilidades en el sistema en caso de alta penetración. Por ello se necesita ganar la confianza de las eléctricas, haciendo que sea una energía predecible, que aporte potencia a la red eléctrica cuando se le pida y que opere participando en la regulación de la frecuencia del sistema eléctrico. Para tal fin, el grupo de investigación de Sistemas Fotovoltaicos, perteneciente al IES de la UPM, está llevando a cabo un proyecto de investigación denominado PV CROPS, financiado por la Comisión Europea, y que tiene por objetivo desarrollar estas estrategias de gestión. En este contexto, el objetivo de este Proyecto Fin de Carrera consiste en implementar un Banco de Ensayos con Integración de Baterías en Sistemas FV Conectados a Red, que permita desarrollar, ensayar y validar estas estrategias. Aprovechando la disponibilidad para usar el Hogar Digital, instalado en la EUITT de la UPM, hemos montado el banco de ensayos en un laboratorio contiguo, y así, poder utilizar este Hogar como un caso real de consumos energéticos de una vivienda. Este banco de ensayos permitirá obtener información de la energía generada por la instalación fotovoltaica y del consumo real de la "casa" anexa, para desarrollar posteriormente estrategias de gestión de la electricidad. El Banco de Ensayos está compuesto por tres bloques principales, interconectados entre sí:  Subsistema de Captación de Datos y Comunicación. Encargado de monitorizar los elementos energéticos y de enviar la información recopilada al Subsistema de Control. Formado por analizadores de red eléctrica, monofásicos y de continua, y una pasarela orientada a la conversión del medio físico Ethernet a RS485.  Subsistema de Control. Punto de observación y recopilación de toda la información que proviene de los elementos energéticos. Es el subsistema donde se crearán y se implementarán estrategias de control energético. Compuesto por un equipo Pxie, controlador empotrado en un chasis de gama industrial, y un equipo PC Host, compuesto por una workstation y tres monitores.  Subsistema de Energía. Formado por los elementos que generan, controlan o consumen energía eléctrica, en el Banco de Ensayos. Constituido por una pérgola FV, un inversor, un inversor bidireccional y un bloque de baterías. El último paso ha sido llevar a cabo un Ejemplo de Aplicación Práctica, con el que hemos probado que el Banco de Ensayos está listo para usarse, es operativo y completamente funcional en operaciones de monitorización de generación energética fotovoltaica y consumo energético. ABSTRACT. The current situation of the energetic market in Spain and the unstoppable increase of the tax on the part of the electrical companies, is promoting the search of alternative sources of energy that allow to the population being able to be supplied of electricity, without having to pay so high costs. To meet this need, the photovoltaic power and above all the self-consumption with injection to network, it is increasingly important inside the energetic world. It allows to the individual not only to pay less for the electricity, in addition it allows to obtain benefits for the energy generated in his own home. But the penetration of this technology in the Electrical Spanish Network has an obstacle, the distrust on the part of the operator of the electrical network, due to the photovoltaic is an intermittent source of energy, which can introduce instabilities in the system in case of high penetration. Therefore it´s necessary to reach the confidence of the electricity companies, making it a predictable energy, which provides with power to the electrical network whenever necessary and that operates taking part in the regulation of the frequency of the electric system. For such an end, the group of system investigation Photovoltaic, belonging to the IES of the UPM, there is carrying out a project of investigation named PV CROPS, financed by the European Commission, and that has for aim to develop these strategies of management. In this context, the objective of this Senior Thesis consists in implementing a Bank of Tests with Integration of Batteries in Photovoltaic Systems Connected to Network, which allows developing, testing and validating these strategies. Taking advantage of the availability to use the Digital Home installed in the EUITT of the UPM, we have mounted the bank of tests in a contiguous laboratory to use this Home as a real case of energetic consumptions of a house. This bank of tests will allow obtaining information of the energy generated by the photovoltaic installation and information of the royal consumption of the attached "house", to develop later strategies of management of the electricity. The Bank of Tests is composed by three principal blocks, interconnected each other:  Subsystem of Gathering of data and Communication. In charge of monitoring the energetic elements and sending the information compiled to the Subsystem of Control. Formed by power analyzers, AC and DC, and a gateway for the conversion of the Ethernet physical medium to RS485.  Subsystem of Control. Point of observation and compilation of all the information that comes from the energetic elements. It is the subsystem where there will be created and there will be implemented strategies of energetic control. Composed of a Pxie, controller fixed in an industrial range chassis, and a PC Host, formed by a workstation and three monitors.  Subsystem of Energy. Formed by the elements of generating, controlling or consuming electric power, in the Bank of Tests. Made of photovoltaic modules, an inverter, a twoway inverter and a batteries block. The last step has been performing an Example of Practical Application we have proved that the Bank of Tests is ready to be used, it´s operative and fully functional in monitoring operations of energetic photovoltaic generation and energetic consumption.

Ion-Ion correlations effect on nonlinear high-frequency plasma conductivity. AT(30-1)-1238-MATT-675

On the basis of the BBGKY hierarchy of equations an expression is derived for the response of a fully ionized plasma to a strong, high-frequency electric field in the limit of infinite ion mass. It is found that even in this limit the ionion correlation function is substantially affected by the field. The corrections to earlier nonlinear results for the current density appear to be quite ssential. The validity of the model introduced by Dawson and Oberman to study the response to a vanishingly small field is confirmed for larger values of the field when the eorrect expression for the ion-ion correlations i s introduced; the model by itself does not yield such an expression. The results have interest for the heating of the plasma and for the propagation of a strong electromagnetic wave through the plasma. The theory seems to be valid for any field intensity for which the plasma is stable.

Photovoltaic LiNbO3particles: Applications to Biomedicine/Biophotonics

Recently, a novel method to trap and pattern ensembles of nanoparticles has been proposed and tested. It relies on the photovoltaic (PV) properties of certain ferroelectric crystals such as LiNbO3 [1,2]. These crystals, when suitably doped, develop very high electric fields in response to illumination with light of suitable wavelength. The PV effect lies in the asymmetrical excitation of electrons giving rise to PV currents and associated space-charge fields (photorefractive effect). The field generated in the bulk of the sample propagates to the surrounding medium as evanescent fields. When dielectric or metal nanoparticles are deposited on the surface of the sample the evanescent fields give rise to either electrophoretic or dielectrophoretic forces, depending on the charge state of the particles, that induce the trapping and patterning effects [3,4]. The purpose of this work has been to explore the effects of such PV fields in the biology and biomedical areas. A first work was able to show the necrotic effects induced by such fields on He-La tumour cells grown on the surface of an illuminated iron-doped LiNbO3 crystal [5]. In principle, it is conceived that LiNbO3 nanoparticles may be advantageously used for such biomedical purposes considering the possibility of such nanoparticles being incorporated into the cells. Previous experiments using microparticles have been performed [5] with similar results to those achieved with the substrate. Therefore, the purpose of this work has been to fabricate and characterize the LiNbO3 nanoparticles and assess their necrotic effects when they are incorporated on a culture of tumour cells. Two different preparation methods have been used: 1) mechanical grinding from crystals, and 2) bottom-up sol-gel chemical synthesis from metal-ethoxide precursors. This later method leads to a more uniform size distribution of smaller particles (down to around 50 nm). Fig. 1(a) and 1(b) shows SEM images of the nanoparticles obtained with both method. An ad hoc software taking into account the physical properties of the crystal, particullarly donor and aceptor concentrations has been developped in order to estimate the electric field generated in noparticles. In a first stage simulations of the electric current of nanoparticles, in a conductive media, due to the PV effect have been carried out by MonteCarlo simulations using the Kutharev 1-centre transport model equations [6] . Special attention has been paid to the dependence on particle size and [Fe2+]/[Fe3+]. First results on cubic particles shows large dispersion for small sizes due to the random number of donors and its effective concentration (Fig 2). The necrotic (toxicity) effect of nanoparticles incorporated into a tumour cell culture subjected to 30 min. illumination with a blue LED is shown in Fig.3. For each type of nanoparticle the percent of cell survival in dark and illumination conditions has been plot as a function of the particle dilution factor. Fig. 1a corresponds to mechanical grinding particles whereas 1b and 1c refer to chemically synthesized particles with two oxidation states. The light effect is larger with mechanical grinding nanoparticles, but dark toxicity is also higher. For chemically synthesized nanoparticles dark toxicity is low but only in oxidized samples, where the PV effect is known to be larger, the light effect is appreciable. These preliminary results demonstrate that Fe:LiNbO· nanoparticles have a biological damaging effect on cells, although there are many points that should be clarified and much space for PV nanoparticles optimization. In particular, it appears necessary to determine the fraction of nanoparticles that become incorporated into the cells and the possible existence of threshold size effects. This work has been supported by MINECO under grant MAT2011-28379-C03.

Diagnostics of classical and dusty plasmas w ith collecting and emissive langmuir probes = Diagnosis de plasmas clásicos y granulares mediante sondas colectoras y emisoras de Langmuir

Las sondas eléctricas se emplean habitualmente en la diagnosis de plasmas. La presente tesis aborda la operación de las sondas colectoras y emisoras de Langmuir en plasmas fríos de baja densidad. El estudio se ha centrado en la determinación del potencial de plasma, Vsp, mediante el potencial flotante de una sonda emisora. Esta técnica consiste en la medida del potencial de la sonda correspondiente a la condición de corriente neta igual a cero, el cual se denomina potencial flotante, VF. Este potencial se desplaza hacia el potencial del plasma según aumenta la emisión termoiónica de la sonda, hasta que se satura cerca de Vsp. Los experimentos llevados a cabo en la pluma de plasma de un motor iónico y en un plasma de descarga de glow muestran que la corriente de electrones termoiónicos es mayor que la corriente de electrones recogidos para una sonda polarizada por debajo del potencial del plasma, resultado inconsistente con la teoría tradicionalmente aceptada. Para investigar estos resultados se ha introducido el parámetro R, definido como el cociente entre la corriente de electrones emitidos y recogidos por la sonda. Este parámetro, que está relacionado con la diferencia de potencial VF - Vsp, también es útil para la descripción de los modos de operación de la sonda emisora (débil, fuerte y más allá del fuerte). Los resultados experimentales evidencian que, al contrario de lo que indica la teoría, R es mayor que la unidad. Esta discrepancia se puede solucionar introduciendo una población efectiva de electrones. Con dicha población, el nuevo modelo para la corriente total de la sonda reproduce los datos experimentales. El origen de este grupo electrónico es todavía una cuestión abierta, pero podría estar originada por una nueva estructura de potencial cerca de la sonda cuando ésta trabaja en el régimen de emisión fuerte. Para explicar dicha estructura de potencial, se propone un modelo unidimensional compuesto por un mínimo de potencial cerca de la superficie de la sonda. El análisis numérico indica que este pozo de potencial aparece para muy altas temperaturas de la sonda, reduciendo la cantidad de electrones emitidos que alcanzan el plasma y evitando así cualquier posible perturbación de éste. Los aspectos experimentales involucrados en el método del potencial flotante también se han estudiado, incluyendo cuestiones como las diferentes técnicas de obtención del VF, el cociente señal-ruido, el acoplamiento de la señal de los equipos utilizados para la obtención de las curvas I-V o la evidencia experimental de los diferentes modos de operación de la sonda. Estas evidencias empíricas se encuentran en todos los aspectos de operación de la sonda: la recolección de electrones, el potencial flotante, la precisión en las curvas I-V y la emisión electrónica. Ésta última también se estudia en la tesis, debido a que un fenómeno de super emisión tiene lugar en el régimen de emisión fuerte. En este modo de operación, las medidas experimentales indican que las corrientes termoiónicas de electrones son mayores que aquéllas predichas por la ecuación de Richardson-Dushman clásica. Por último, la diagnosis de plasmas usando sondas eléctrica bajo presencia de granos de polvo (plasmas granulares) en plasmas fríos de baja densidad también se ha estudiado, mediante la aplicación numérica de la técnica del potencial flotante de la sonda emisora en un plasma no convencional. Los resultados apuntan a que el potencial flotante de una sonda emisora se vería afectado por altas densidades de polvo o grandes partículas. ABSTRACT Electric probes are widely employed for plasma diagnostics. This dissertation concerns the operation of collecting and emissive Langmuir probes in low density cold plasmas. The study is focused on the determination of the plasma potential, Vsp, by means of the floating potential of emissive probes. This technique consists of the measurement of the probe potential, corresponding to the zero net probe current, which is the so-called floating potential, VF . This potential displaces towards the plasma potential as the thermionic electron emission increases, until it saturates near Vsp. Experiments carried out in the plasma plume of an ion thruster and in a glow discharge plasma show the thermionic electron current of the emissive Langmuir probe is higher than the collected electron current, for a probe with a bias potential below Vsp, which is inconsistent with the traditional accepted theory. To investigate these results, a parameter R is introduced as the ratio between the emitted and the collected electron current. This parameter, which is related to the difference VF - Vsp, is also useful for the description of the operation modes of the emissive Langmuir probe (weak, strong and beyond strong). The experimental results give an inconsistency of R > 1, which is solved by a modification of the theory for emissive probes, with the introduction of an effective electron population. With this new electron group, the new model for the total probe current agrees with the experimental data. The origin of this electron group remains an open question, but it might be originated by a new potential structure near the emissive probe when it operates in the strong emission regime. A simple one-dimension model composed by a minimum of potential near the probe surface is discussed for strongly emitting emissive probes. The results indicate that this complex potential structure appears for very high probe temperatures and the potential well might reduce the emitted electrons population reaching the plasma bulk. The experimental issues involved in the floating potential method are also studied, as the different obtaining techniques of VF, the signal-to-noise ratio, the signal coupling of the I-V curve measurement system or the experimental evidence of the probe operation modes. These empirical proofs concern all the probe operation aspects: the electron collection, the floating potential, the I-V curve accuracy as well as the electron emission. This last issue is also investigated in this dissertation, because a super emission takes place in the strong emission regime. In this operation mode, the experimental results indicate that the thermionic electron currents might be higher than those predicted by the classical Richardson-Dushman equation. Finally, plasma diagnosis using electric probes in the presence of dust grains (dusty plasmas) in low density cold plasmas is also addressed. The application of the floating potential technique of the emissive probe in a non-conventional complex plasma is numerically investigated, whose results point out the floating potential of the emissive probe might be shifted for high dust density or large dust particles.

Análisis y simulación numérica de problemas electrohidrodinámicos relacionados con el electrospray

La presente tesis es un estudio analítico y numérico del electrospray. En la configuración más sencilla, un caudal constante del líquido a atomizar, que debe tener una cierta conductividad eléctrica, se inyecta en un medio dieléctrico (un gas u otro líquido inmiscible con el primero) a través de un tubo capilar metálico. Entre este tubo y un electrodo lejano se aplica un voltaje continuo que origina un campo eléctrico en el líquido conductor y en el espacio que lo rodea. El campo eléctrico induce una corriente eléctrica en el líquido, que acumula carga en su superficie, y da lugar a un esfuerzo eléctrico sobre la superficie, que tiende a alargarla en la dirección del campo eléctrico. El líquido forma un menisco en el extremo del tubo capilar cuando el campo eléctrico es suficientemente intenso y el caudal suficientemente pequeño. Las variaciones de presión y los esfuerzos viscosos asociados al movimiento del líquido son despreciables en la mayor parte de este menisco, siendo dominantes los esfuerzos eléctrico y de tensión superficial que actúan sobre la superficie del líquido. En el modo de funcionamiento llamado de conochorro, el balance de estos esfuerzos hace que el menisco adopte una forma cónica (el cono de Taylor) en una región intermedia entre el extremo del tubo y la punta del menisco. La velocidad del líquido aumenta al acercarse al vértice del cono, lo cual propicia que las variaciones de la presión en el líquido generadas por la inercia o por la viscosidad entren en juego, desequilibrando el balance de esfuerzos mencionado antes. Como consecuencia, del vértice del cono sale un delgado chorro de líquido, que transporta la carga eléctrica que se acumula en la superficie. La acción del campo eléctrico tangente a la superficie sobre esta carga origina una tracción eléctrica que tiende a alargar el chorro. Esta tracción no es relevante en el menisco, donde el campo eléctrico tangente a la superficie es muy pequeño, pero se hace importante en el chorro, donde es la causa del movimiento del líquido. Lejos del cono, el chorro puede o bien desarrollar una inestabilidad asimétrica que lo transforma en una espiral (whipping) o bien romperse en un spray de gotas prácticamente monodispersas cargadas eléctricamente. La corriente eléctrica transportada por el líquido es la suma de la corriente de conducción en el interior del líquido y la corriente debida a la convección de la carga acumulada en su superficie. La primera domina en el menisco y la segunda en el chorro lejano, mientras que las dos son comparables en una región intermedia de transferencia de corriente situada al comienzo del chorro aunque aguas abajo de la región de transición cono-chorro, en la que el menisco deja de ser un cono de Taylor. Para un campo exterior dado, la acumulación de carga eléctrica en la superficie del líquido reduce el campo eléctrico en el interior del mismo, que llega a anularse cuando la carga alcanza un estado final de equilibrio. El tiempo característico de este proceso es el tiempo de relajación dieléctrica, que es una propiedad del líquido. Cuando el tiempo de residencia del líquido en la región de transición cono-chorro (o en otra región del campo fluido) es grande frente al tiempo de relajación dieléctrica, la carga superficial sigue una sucesión de estados de equilibrio y apantalla al líquido del campo exterior. Cuando esta condición deja de cumplirse, aparecen efectos de relajación de carga, que se traducen en que el campo exterior penetra en el líquido, a no ser que su constante dieléctrica sea muy alta, en cuyo caso el campo inducido por la carga de polarización evita la entrada del campo exterior en el menisco y en una cierta región del chorro. La carga eléctrica en equilibrio en la superficie de un menisco cónico intensifica el campo eléctrico y determina su variación espacial hasta distancias aguas abajo del menisco del orden de su tamaño. Este campo, calculado por Taylor, es independiente del voltaje aplicado, por lo que las condiciones locales del flujo y el valor de la corriente eléctrica son también independientes del voltaje en tanto los tamaños de las regiones que determinan estas propiedades sean pequeños frente al tamaño del menisco. Los resultados experimentales publicados en la literatura muestran que existe un caudal mínimo para el que el modo cono-chorro que acabamos de describir deja de existir. El valor medio y la desviación típica de la distribución de tamaños de las gotas generadas por un electrospray son mínimos cuando se opera cerca del caudal mínimo. A pesar de que los mecanismos responsables del caudal mínimo han sido muy estudiados, no hay aún una teoría completa del mismo, si bien su existencia parece estar ligada a la aparición de efectos de relajación de carga en la región de transición cono-chorro. En esta tesis, se presentan estimaciones de orden de magnitud, algunas existentes y otras nuevas, que muestran los balances dominantes responsables de las distintas regiones de la estructura asintótica de la solución en varios casos de interés. Cuando la inercia del líquido juega un papel en la transición cono-chorro, los resultados muestran que la región de transferencia de corriente, donde la mayor parte de la corriente pasa a la superficie, está en el chorro aguas abajo de la región de transición cono-chorro. Los efectos de relajación de carga aparecen de forma simultánea en el chorro y la región de transición cuando el caudal se disminuye hasta valores de un cierto orden. Para caudales aún menores, los efectos de relajación de carga se notan en el menisco, en una región grande comparada con la de transición cono-chorro. Cuando el efecto de las fuerzas de viscosidad es dominante en la región de transición, la región de transferencia de corriente está en el chorro pero muy próxima a la región de transición cono-chorro. Al ir disminuyendo el caudal, los efectos de relajación de carga aparecen progresivamente en el chorro, en la región de transición y por último en el menisco. Cuando el caudal es mucho mayor que el mínimo del modo cono-chorro, el menisco deja de ser cónico. El campo eléctrico debido al voltaje aplicado domina en la región de transferencia de corriente, y tanto la corriente eléctrica como el tamaño de las diferentes regiones del problema pasan a depender del voltaje aplicado. Como resultado de esta dependencia, el plano caudal-voltaje se divide en diferentes regiones que se analizan separadamente. Para caudales suficientemente grandes, la inercia del líquido termina dominando frente a las fuerzas de la viscosidad. Estos resultados teóricos se han validado con simulaciones numéricas. Para ello se ha formulado un modelo simplificado del flujo, el campo eléctrico y el transporte de carga en el menisco y el chorro del electrospray. El movimiento del líquido se supone casi unidireccional y se describe usando la aproximación de Cosserat para un chorro esbelto. Esta aproximación, ampliamente usada en la literatura, permite simular con relativa facilidad múltiples casos y cubrir amplios rangos de valores de los parámetros reteniendo los efectos de la viscosidad y la inercia del líquido. Los campos eléctricos dentro y fuera del liquido están acoplados y se calculan sin simplificación alguna usando un método de elementos de contorno. La solución estacionaria del problema se calcula mediante un método iterativo. Para explorar el espacio de los parámetros, se comienza calculando una solución para valores fijos de las propiedades del líquido, el voltaje aplicado y el caudal. A continuación, se usa un método de continuación que permite delinear la frontera del dominio de existencia del modo cono-chorro, donde el método iterativo deja de converger. Cuando el efecto de la inercia del líquido domina en la región de transición cono-chorro, el caudal mínimo para el cual el método iterativo deja de converger es del orden del valor estimado del caudal para el que comienza a haber efectos de relajación de carga en el chorro y el cono. Aunque las simulaciones no convergen por debajo de dicho caudal, el valor de la corriente eléctrica para valores del caudal ligeramente mayores parece ajustarse a las estimaciones para caudales menores, reflejando un posible cambio en los balances aplicables. Por el contrario, cuando las fuerzas viscosas dominan en la región de transición, se pueden obtener soluciones estacionarias para caudales bastante menores que aquel para el que aparecen efectos de relajación de carga en la región de transición cono-chorro. Los resultados numéricos obtenidos para estos pequeños caudales se ajustan perfectamente a las estimaciones de orden de magnitud que se describen en la memoria. Por último, se incluyen como anexos dos estudios teóricos que han surgido de forma natural durante el desarrollo de la tesis. El primero hace referencia a la singularidad en el campo eléctrico que aparece en la línea de contacto entre el líquido y el tubo capilar en la mayoría de las simulaciones. Primero se estudia en qué situaciones el campo eléctrico tiende a infinito en la línea de contacto. Después, se comprueba que dicha singularidad no supone un fallo en la descripción del problema y que además no afecta a la solución lejos de la línea de contacto. También se analiza si los esfuerzos eléctricos infinitamente grandes a los que da lugar dicha singularidad pueden ser compensados por el resto de esfuerzos que actúan en la superficie del líquido. El segundo estudio busca determinar el tamaño de la región de apantallamiento en un chorro de líquido dieléctrico sin carga superficial. En esta región, el campo exterior es compensado parcialmente por el campo que induce la carga de polarización en la superficie del líquido, de forma que en el interior del líquido el campo eléctrico es mucho menor que en el exterior. Una región como ésta aparece en las estimaciones cuando los efectos de relajación de carga son importantes en la región de transferencia de corriente en el chorro. ABSTRACT This aim of this dissertation is a theoretical and numerical analysis of an electrospray. In its most simple configuration, a constant flow rate of the liquid to be atomized, which has to be an electrical conductor, is injected into a dielectric medium (a gas or another inmiscible fluid) through a metallic capillary tube. A constant voltage is applied between this tube and a distant electrode that produces an electric field in the liquid and the surrounding medium. This electric field induces an electric current in the liquid that accumulates charge at its surface and leads to electric stresses that stretch the surface in the direction of the electric field. A meniscus appears on the end of the capillary tube when the electric field is sufficiently high and the flow rate is small. Pressure variations and viscous stresses due to the motion of the liquid are negligible in most of the meniscus, where normal electric and surface tension stresses acting on the surface are dominant. In the so-called cone-jet mode, the balance of these stresses forces the surface to adopt a conical shape -Taylor cone- in a intermediate region between the end of the tube and the tip of the meniscus. When approaching the cone apex, the velocity of the liquid increases and leads to pressure variations that eventually disturb the balance of surfaces tension and electric stresses. A thin jet emerges then from the tip of the meniscus that transports the charge accumulated at its surface. The electric field tangent to the surface of the jet acts on this charge and continuously stretches the jet. This electric force is negligible in the meniscus, where the component of the electric field tangent to the surface is small, but becomes very important in the jet. Far from the cone, the jet can either develop an asymmetrical instability named “whipping”, whereby the jet winds into a spiral, or break into a spray of small, nearly monodisperse, charged droplets. The electric current transported by the liquid has two components, the conduction current in the bulk of the liquid and the convection current due to the transport of the surface charge by the flow. The first component dominates in the meniscus, the second one in the far jet, and both are comparable in a current transfer region located in the jet downstream of the cone-jet transition region where the meniscus ceases to be a Taylor cone. Given an external electric field, the charge that accumulates at the surface of the liquid reduces the electric field inside the liquid, until an equilibrium is reached in which the electric field induced by the surface charge counters the external electric field and shields the liquid from this field. The characteristic time of this process is the electric relaxation time, which is a property of the liquid. When the residence time of the liquid in the cone-jet transition region (or in other region of the flow) is greater than the electric relaxation time, the surface charge follows a succession of equilibrium states and continuously shield the liquid from the external field. When this condition is not satisfied, charge relaxation effects appear and the external field penetrates into the liquid unless the liquid permittivity is large. For very polar liquids, the field due to the polarization charge at the surface prevents the external field from entering the liquid in the cone and in certain region of the jet. The charge at the surface of a conical meniscus intensifies the electric field around the cone, determining its spatial variation up to distances downstream of the apex of the order of the size of the meniscus. This electric field, first computed by Taylor, is independent of the applied voltage. Therefore local flow characteristics and the electric current carried by the jet are also independent of the applied voltage provided the size of the regions that determine these magnitudes are small compared with the size of the meniscus. Many experiments in the literature show the existence of a minimum flow rate below which the cone-jet mode cannot be established. The mean value and the standard deviation of the electrospray droplet size distribution are minimum when the device is operated near the minimum flow rate. There is no complete explanation of the minimum flow rate, even though possible mechanisms have been extensively studied. The existence of a minimum flow rate seems to be connected with the appearance of charge relaxation effects in the transition region. In this dissertation, order of magnitude estimations are worked out that show the dominant balances in the different regions of the asymptotic structure of the solution for different conditions of interest. When the inertia of the liquid plays a role in the cone-jet transition region, the region where most of the electric current is transfered to the surface lies in the jet downstream the cone-jet transition region. When the flow rate decreases to a certain value, charge relaxation effects appear simultaneously in the jet and in the transition region. For smaller values of the flow rate, charge relaxation effects are important in a region of the meniscus larger than the transition region. When viscous forces dominate in the flow in the cone-jet transition region, the current transfer region is located in the jet immediately after the transition region. When flow rate is decreased, charge relaxation effects appears gradually, first in the jet, then in the transition region, and finally in the meniscus. When flow rate is much larger than the cone-jet mode minimum, the meniscus ceases to be a cone. The electric current and the structure of the solution begin to depend on the applied voltage. The flow rate-voltage plane splits into different regions that are analyzed separately. For sufficiently large flow rates, the effect of the inertia of the liquid always becomes greater than the effect of the viscous forces. A set of numerical simulations have been carried out in order to validate the theoretical results. A simplified model of the problem has been devised to compute the flow, the electric field and the surface charge in the meniscus and the jet of an electrospray. The motion of the liquid is assumed to be quasi-unidirectional and described by Cosserat’s approximation for a slender jet. This widely used approximation allows to easily compute multiple configurations and to explore wide ranges of values of the governing parameters, retaining the effects of the viscosity and the inertia of the liquid. Electric fields inside and outside the liquid are coupled and are computed without any simplification using a boundary elements method. The stationary solution of the problem is obtained by means of an iterative method. To explore the parameter space, a solution is first computed for a set of values of the liquid properties, the flow rate and the applied voltage, an then a continuation method is used to find the boundaries of the cone-jet mode domain of existence, where the iterative method ceases to converge. When the inertia of the liquid dominates in the cone-jet transition region, the iterative method ceases to converge for values of the flow rate for which order-of-magnitude estimates first predict charge relaxation effects to be important in the cone and the jet. The electric current computed for values of the flow rate slightly above the minimum for which convergence is obtained seems to agree with estimates worked out for lower flow rates. When viscous forces dominate in the transition region, stationary solutions can be obtained for flow rates significantly smaller than the one for which charge relaxation effects first appear in the transition region. Numerical results obtained for those small values of the flow rate agree with our order of magnitude estimates. Theoretical analyses of two issues that have arisen naturally during the thesis are summarized in two appendices. The first appendix contains a study of the singularity of the electric field that most of the simulations show at the contact line between the liquid and the capillary tube. The electric field near the contact line is analyzed to determine the ranges of geometrical configurations and liquid permittivity where a singularity appears. Further estimates show that this singularity does not entail a failure in the description of the problem and does not affect the solution far from the contact line. The infinite electric stresses that appear at the contact line can be effectively balanced by surface tension. The second appendix contains an analysis of the size and slenderness of the shielded region of a dielectric liquid in the absence of free surface charge. In this region, the external electric field is partially offset by the polarization charge so that the inner electric field is much lower than the outer one. A similar region appears in the estimates when charge relaxation effects are important in the current transfer region.

A Novel Ground Fault Identification Method for 2 x 5 kV Railway Power Supply Systems

The location of ground faults in railway electric lines in 2 × 5 kV railway power supply systems is a difficult task. In both 1 × 25 kV and transmission power systems it is common practice to use distance protection relays to clear ground faults and localize their positions. However, in the particular case of this 2 × 25 kV system, due to the widespread use of autotransformers, the relation between the distance and the impedance seen by the distance protection relays is not linear and therefore the location is not accurate enough. This paper presents a simple and economical method to identify the subsection between autotransformers and the conductor (catenary or feeder) where the ground fault is happening. This method is based on the comparison of the angle between the current and the voltage of the positive terminal in each autotransformer. Consequently, after the identification of the subsection and the conductor with the ground defect, only the subsection where the ground fault is present will be quickly removed from service, with the minimum effect on rail traffic. This method has been validated through computer simulations and laboratory tests with positive results.