Design and Optimization of Power Delivery and Distribution Systems Using Evolutionary Computation Techniques

Nowadays computing platforms consist of a very large number of components that require to be supplied with diferent voltage levels and power requirements. Even a very small platform, like a handheld computer, may contain more than twenty diferent loads and voltage regulators. The power delivery designers of these systems are required to provide, in a very short time, the right power architecture that optimizes the performance, meets electrical specifications plus cost and size targets. The appropriate selection of the architecture and converters directly defines the performance of a given solution. Therefore, the designer needs to be able to evaluate a significant number of options in order to know with good certainty whether the selected solutions meet the size, energy eficiency and cost targets. The design dificulties of selecting the right solution arise due to the wide range of power conversion products provided by diferent manufacturers. These products range from discrete components (to build converters) to complete power conversion modules that employ diferent manufacturing technologies. Consequently, in most cases it is not possible to analyze all the alternatives (combinations of power architectures and converters) that can be built. The designer has to select a limited number of converters in order to simplify the analysis. In this thesis, in order to overcome the mentioned dificulties, a new design methodology for power supply systems is proposed. This methodology integrates evolutionary computation techniques in order to make possible analyzing a large number of possibilities. This exhaustive analysis helps the designer to quickly define a set of feasible solutions and select the best trade-off in performance according to each application. The proposed approach consists of two key steps, one for the automatic generation of architectures and other for the optimized selection of components. In this thesis are detailed the implementation of these two steps. The usefulness of the methodology is corroborated by contrasting the results using real problems and experiments designed to test the limits of the algorithms.

Organisational learning, strategic rigidity and technology adoption: Implications for electric utilities and renewable energy firms

This paper examines the implications of strategic rigidness for technology adoption behaviours among electric utilities. Such behaviours lead to heterogeneity in firm performance and consequently affect the electric utility industry. The paper's central aim is to identify and describe the implications of strategic rigidness for a utility firm's decision making in adopting newer renewable energy technologies. The findings indicate that not all utility firms are keen to adopt these new technologies, as these firms have traditionally been operating efficiently with a more conventional and mature technological arrangement that has become embedded in the organisational routine. Case studies of Iberdrola S.A. and Enel S.p.A. as major electric utilities are detailed to document mergers and acquisitions and technology adoption decisions. The results indicate that technology adoption behaviours vary widely across utility firms with different organisational learning processes and core capabilities.

Ion correlations due to high-frequency electric field and their effect on the nonlinear plasma conductivity

The influence of a strong, high‐frequency electric field on the ion‐ion correlations in a fully ionized plasma is investigated in the limit of infinite ion mass, starting with the Bogoliubov‐Born‐Green‐Kirkwood‐Yvon hierarchy of equations; a significant departure from the thermal correlations is found. It is shown that the above effect may substantially modify earlier results on the nonlinear high‐frequency plasma conductivity.

Morphology and distribution of volcanic bombs in Caldera Quemada de Arriba (Lanzarote, Canary Islands): implications for volcanic hazard analysis

Análisis del riesgo volcánico. We show the preliminary results of the study of 561 volcanic bombs ejected from a pyroclastic cone during the 1730-1736 Timanfaya eruption (Lanzarote, Canary Islands). This cone displays the highest concentration of big bombs (major axis higher than 1 m) of Timanfaya. More than 560 bombs have been studied to calculate their reach. The results suggest that bombs of 1t have a reach of 409 m, while bombs up to 28 t have a reach of 248 m. These data may be used to define a security area once a vent has been opened, but also to calculate other data such the initial velocity of ejection. The geomorphological analysis and the study of the deposits also contribute to better understand an undocumented episode of the Timanfaya eruption and also provide important data for volcanic bombs modeling for volcanic hazard analysis.

Thermal, stress, and traps effects in AlGaN/GaN HEMTs

GaN y AlN son materiales semiconductores piezoeléctricos del grupo III-V. La heterounión AlGaN/GaN presenta una elevada carga de polarización tanto piezoeléctrica como espontánea en la intercara, lo que genera en su cercanía un 2DEG de grandes concentración y movilidad. Este 2DEG produce una muy alta potencia de salida, que a su vez genera una elevada temperatura de red. Las tensiones de puerta y drenador provocan un stress piezoeléctrico inverso, que puede afectar a la carga de polarización piezoeléctrica y así influir la densidad 2DEG y las características de salida. Por tanto, la física del dispositivo es relevante para todos sus aspectos eléctricos, térmicos y mecánicos. En esta tesis se utiliza el software comercial COMSOL, basado en el método de elementos finitos (FEM), para simular el comportamiento integral electro-térmico, electro-mecánico y electro-térmico-mecánico de los HEMTs de GaN. Las partes de acoplamiento incluyen el modelo de deriva y difusión para el transporte electrónico, la conducción térmica y el efecto piezoeléctrico. Mediante simulaciones y algunas caracterizaciones experimentales de los dispositivos, hemos analizado los efectos térmicos, de deformación y de trampas. Se ha estudiado el impacto de la geometría del dispositivo en su auto-calentamiento mediante simulaciones electro-térmicas y algunas caracterizaciones eléctricas. Entre los resultados más sobresalientes, encontramos que para la misma potencia de salida la distancia entre los contactos de puerta y drenador influye en generación de calor en el canal, y así en su temperatura. El diamante posee une elevada conductividad térmica. Integrando el diamante en el dispositivo se puede dispersar el calor producido y así reducir el auto-calentamiento, al respecto de lo cual se han realizado diversas simulaciones electro-térmicas. Si la integración del diamante es en la parte superior del transistor, los factores determinantes para la capacidad disipadora son el espesor de la capa de diamante, su conductividad térmica y su distancia a la fuente de calor. Este procedimiento de disipación superior también puede reducir el impacto de la barrera térmica de intercara entre la capa adaptadora (buffer) y el substrato. La muy reducida conductividad eléctrica del diamante permite que pueda contactar directamente el metal de puerta (muy cercano a la fuente de calor), lo que resulta muy conveniente para reducir el auto-calentamiento del dispositivo con polarización pulsada. Por otra parte se simuló el dispositivo con diamante depositado en surcos atacados sobre el sustrato como caminos de disipación de calor (disipador posterior). Aquí aparece una competencia de factores que influyen en la capacidad de disipación, a saber, el surco atacado contribuye a aumentar la temperatura del dispositivo debido al pequeño tamaño del disipador, mientras que el diamante disminuiría esa temperatura gracias a su elevada conductividad térmica. Por tanto, se precisan capas de diamante relativamente gruesas para reducer ele efecto de auto-calentamiento. Se comparó la simulación de la deformación local en el borde de la puerta del lado cercano al drenador con estructuras de puerta estándar y con field plate, que podrían ser muy relevantes respecto a fallos mecánicos del dispositivo. Otras simulaciones se enfocaron al efecto de la deformación intrínseca de la capa de diamante en el comportamiento eléctrico del dispositivo. Se han comparado los resultados de las simulaciones de la deformación y las características eléctricas de salida con datos experimentales obtenidos por espectroscopía micro-Raman y medidas eléctricas, respectivamente. Los resultados muestran el stress intrínseco en la capa producido por la distribución no uniforme del 2DEG en el canal y la región de acceso. Además de aumentar la potencia de salida del dispositivo, la deformación intrínseca en la capa de diamante podría mejorar la fiabilidad del dispositivo modulando la deformación local en el borde de la puerta del lado del drenador. Finalmente, también se han simulado en este trabajo los efectos de trampas localizados en la superficie, el buffer y la barrera. Las medidas pulsadas muestran que tanto las puertas largas como las grandes separaciones entre los contactos de puerta y drenador aumentan el cociente entre la corriente pulsada frente a la corriente continua (lag ratio), es decir, disminuir el colapse de corriente (current collapse). Este efecto ha sido explicado mediante las simulaciones de los efectos de trampa de superficie. Por su parte, las referidas a trampas en el buffer se enfocaron en los efectos de atrapamiento dinámico, y su impacto en el auto-calentamiento del dispositivo. Se presenta también un modelo que describe el atrapamiento y liberación de trampas en la barrera: mientras que el atrapamiento se debe a un túnel directo del electrón desde el metal de puerta, el desatrapamiento consiste en la emisión del electrón en la banda de conducción mediante túnel asistido por fonones. El modelo también simula la corriente de puerta, debida a la emisión electrónica dependiente de la temperatura y el campo eléctrico. Además, también se ilustra la corriente de drenador dependiente de la temperatura y el campo eléctrico. ABSTRACT GaN and AlN are group III-V piezoelectric semiconductor materials. The AlGaN/GaN heterojunction presents large piezoelectric and spontaneous polarization charge at the interface, leading to high 2DEG density close to the interface. A high power output would be obtained due to the high 2DEG density and mobility, which leads to elevated lattice temperature. The gate and drain biases induce converse piezoelectric stress that can influence the piezoelectric polarization charge and further influence the 2DEG density and output characteristics. Therefore, the device physics is relevant to all the electrical, thermal, and mechanical aspects. In this dissertation, by using the commercial finite-element-method (FEM) software COMSOL, we achieved the GaN HEMTs simulation with electro-thermal, electro-mechanical, and electro-thermo-mechanical full coupling. The coupling parts include the drift-diffusion model for the electron transport, the thermal conduction, and the piezoelectric effect. By simulations and some experimental characterizations, we have studied the device thermal, stress, and traps effects described in the following. The device geometry impact on the self-heating was studied by electro-thermal simulations and electrical characterizations. Among the obtained interesting results, we found that, for same power output, the distance between the gate and drain contact can influence distribution of the heat generation in the channel and thus influence the channel temperature. Diamond possesses high thermal conductivity. Integrated diamond with the device can spread the generated heat and thus potentially reduce the device self-heating effect. Electro-thermal simulations on this topic were performed. For the diamond integration on top of the device (top-side heat spreading), the determinant factors for the heat spreading ability are the diamond thickness, its thermal conductivity, and its distance to the heat source. The top-side heat spreading can also reduce the impact of thermal boundary resistance between the buffer and the substrate on the device thermal behavior. The very low electrical conductivity of diamond allows that it can directly contact the gate metal (which is very close to the heat source), being quite convenient to reduce the self-heating for the device under pulsed bias. Also, the diamond coated in vias etched in the substrate as heat spreading path (back-side heat spreading) was simulated. A competing mechanism influences the heat spreading ability, i.e., the etched vias would increase the device temperature due to the reduced heat sink while the coated diamond would decrease the device temperature due to its higher thermal conductivity. Therefore, relative thick coated diamond is needed in order to reduce the self-heating effect. The simulated local stress at the gate edge of the drain side for the device with standard and field plate gate structure were compared, which would be relevant to the device mechanical failure. Other stress simulations focused on the intrinsic stress in the diamond capping layer impact on the device electrical behaviors. The simulated stress and electrical output characteristics were compared to experimental data obtained by micro-Raman spectroscopy and electrical characterization, respectively. Results showed that the intrinsic stress in the capping layer caused the non-uniform distribution of 2DEG in the channel and the access region. Besides the enhancement of the device power output, intrinsic stress in the capping layer can potentially improve the device reliability by modulating the local stress at the gate edge of the drain side. Finally, the surface, buffer, and barrier traps effects were simulated in this work. Pulsed measurements showed that long gates and distances between gate and drain contact can increase the gate lag ratio (decrease the current collapse). This was explained by simulations on the surface traps effect. The simulations on buffer traps effects focused on illustrating the dynamic trapping/detrapping in the buffer and the self-heating impact on the device transient drain current. A model was presented to describe the trapping and detrapping in the barrier. The trapping was the electron direct tunneling from the gate metal while the detrapping was the electron emission into the conduction band described by phonon-assisted tunneling. The reverse gate current was simulated based on this model, whose mechanism can be attributed to the temperature and electric field dependent electron emission in the barrier. Furthermore, the mechanism of the device bias via the self-heating and electric field impact on the electron emission and the transient drain current were also illustrated.

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.

Bare-tether sheath and current: comparison of asymptotic theory and kinetic simulations in stationary plasma

Analytical expressions for current to a cylindrical Langmuir probe at rest in unmagnetized plasma are compared with results from both steady-state Vlasov and particle-in-cell simulations. Probe bias potentials that are much greater than plasma temperature (assumed equal for ions and electrons), as of interest for bare conductive tethers, are considered. At a very high bias, both the electric potential and the attracted-species density exhibit complex radial profiles; in particular, the density exhibits a minimum well within the plasma sheath and a maximum closer to the probe. Excellent agreement is found between analytical and numerical results for values of the probe radiusR close to the maximum radius Rmax for orbital-motion-limited (OML) collection at a particular bias in the following number of profile features: the values and positions of density minimum and maximum, position of sheath boundary, and value of a radius characterizing the no-space-charge behavior of a potential near the high-bias probe. Good agreement between the theory and simulations is also found for parametric laws jointly covering the following three characteristic R ranges: sheath radius versus probe radius and bias for Rmax; density minimum versus probe bias for Rmax; and (weakly bias-dependent) current drop below the OML value versus the probe radius for R > Rmax.

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.

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.

Analysis and Design Considerations of an Electric Vehicle Powertrain regarding Energy Efficiency and Magnetic Field Exposure

En esta tesis se analiza el sistema de tracción de un vehículo eléctrico de batería desde el punto de vista de la eficiencia energética y de la exposición a campos magnéticos por parte de los pasajeros (radiación electromagnética). Este estudio incluye tanto el sistema de almacenamiento de energía como la máquina eléctrica, junto con la electrónica de potencia y los sistemas de control asociados a ambos. Los análisis y los resultados presentados en este texto están basados en modelos matemáticos, simulaciones por ordenador y ensayos experimentales a escala de laboratorio. La investigación llevada a cabo durante esta tesis tuvo siempre un marcado enfoque industrial, a pesar de estar desarrollada en un entorno de considerable carácter universitario. Las líneas de investigación acometidas tuvieron como destinatario final al diseñador y al fabricante del vehículo, a pesar de lo cual algunos de los resultados obtenidos son preliminares y/o excesivamente académicos para resultar de interés industrial. En el ámbito de la eficiencia energética, esta tesis estudia sistemas híbridos de almacenamiento de energía basados en una combinación de baterías de litio y supercondensadores. Este tipo de sistemas son analizados desde el punto de vista de la eficiencia mediante modelos matemáticos y simulaciones, cuantificando el impacto de ésta en otros parámetros tales como el envejecimiento de las baterías. Respecto a la máquina eléctrica, el estudio se ha centrado en máquinas síncronas de imanes permanentes. El análisis de la eficiencia considera tanto el diseño de la máquina como la estrategia de control, dejando parcialmente de lado el inversor y la técnica de modulación (que son incluidos en el estudio como fuentes adicionales de pérdidas, pero no como potenciales fuentes de optimización de la eficiencia). En este sentido, tanto la topología del inversor (trifásico, basado en IGBTs) como la técnica de modulación (control de corriente en banda de histéresis) se establecen desde el principio. El segundo aspecto estudiado en esta tesis es la exposición a campos magnéticos por parte de los pasajeros. Este tema se enfoca desde un punto de vista predictivo, y no desde un punto de vista de diagnóstico, puesto que se ha desarrollado una metodología para estimar el campo magnético generado por los dispositivos de potencia de un vehículo eléctrico. Esta metodología ha sido validada mediante ensayos de laboratorio. Otros aspectos importantes de esta contribución, además de la metodología en sí misma, son las consecuencias que se derivan de ella (por ejemplo, recomendaciones de diseño) y la comprensión del problema proporcionada por esta. Las principales contribuciones de esta tesis se listan a continuación: una recopilación de modelos de pérdidas correspondientes a la mayoría de dispositivos de potencia presentes en un vehículo eléctrico de batería, una metodología para analizar el funcionamiento de un sistema híbrido de almacenamiento de energía para aplicaciones de tracción, una explicación de cómo ponderar energéticamente los puntos de operación par-velocidad de un vehículo eléctrico (de utilidad para evaluar el rendimiento de una máquina eléctrica, por ejemplo), una propuesta de incluir un convertidor DC-DC en el sistema de tracción para minimizar las pérdidas globales del accionamiento (a pesar de las nuevas pérdidas introducidas por el propio DC-DC), una breve comparación entre dos tipos distintos de algoritmos de minimización de pérdidas para máquinas síncronas de imanes permanentes, una metodología predictiva para estimar la exposición a campos magnéticos por parte de los pasajeros de un vehículo eléctrico (debida a los equipos de potencia), y finalmente algunas conclusiones y recomendaciones de diseño respecto a dicha exposición a campos magnéticos. ABSTRACT This dissertation analyzes the powertrain of a battery electric vehicle, focusing on energy efficiency and passenger exposure to electromagnetic fields (electromagnetic radiation). This study comprises the energy storage system as well as the electric machine, along with their associated power electronics and control systems. The analysis and conclusions presented in this dissertation are based on mathematical models, computer simulations and laboratory scale tests. The research performed during this thesis was intended to be of industrial nature, despite being developed in a university. In this sense, the work described in this document was carried out thinking of both the designer and the manufacturer of the vehicle. However, some of the results obtained lack industrial readiness, and therefore they remain utterly academic. Regarding energy efficiency, hybrid energy storage systems consisting in lithium batteries, supercapacitors and up to two DC-DC power converters are considered. These kind of systems are analyzed by means of mathematical models and simulations from the energy efficiency point of view, quantifying its impact on other relevant aspects such as battery aging. Concerning the electric machine, permanent magnet synchronous machines are studied in this work. The energy efficiency analysis comprises the machine design and the control strategy, while the inverter and its modulation technique are taken into account but only as sources of further power losses, and not as potential sources for further efficiency optimization. In this sense, both the inverter topology (3-phase IGBT-based inverter) and the switching technique (hysteresis current control) are fixed from the beginning. The second aspect studied in this work is passenger exposure to magnetic fields. This topic is approached from the prediction point of view, rather than from the diagnosis point of view. In other words, a methodology to estimate the magnetic field generated by the power devices of an electric vehicle is proposed and analyzed in this dissertation. This methodology has been validated by laboratory tests. The most important aspects of this contribution, apart from the methodology itself, are the consequences (for instance, design guidelines) and the understanding of the magnetic radiation issue provided by it. The main contributions of this dissertation are listed next: a compilation of loss models for most of the power devices found in a battery electric vehicle powertrain, a simulation-based methodology to analyze hybrid energy storage performance in traction applications, an explanation of how to assign energy-based weights to different operating points in traction drives (useful when assessing electrical machine performance, for instance), a proposal to include one DC-DC converter in electric powertrains to minimize overall power losses in the system (despite the new losses added by the DC-DC), a brief comparison between two kinds of loss-minimization algorithms for permanent magnet synchronous machines in terms of adaptability and energy efficiency, a predictive methodology to estimate passenger magnetic field exposure due to power devices in an electric vehicle, and finally some useful conclusions and design guidelines concerning magnetic field exposure.