Investigation into the performance of an algorithm for deriving concise descriptions of optic flow fields for real-time control

This paper describes a region-based algorithm for deriving a concise description of a first order optical flow field. The algorithm described achieves performance improvements over existing algorithms without compromising the accuracy of the flow field values calculated. These improvements are brought about by not computing the entire flow field between two consecutive images, but by considering only the flow vectors of a selected subset of the images. The algorithm is presented in the context of a project to balance a bipedal robot using visual information.

The role of the harmonic vector average in motion integration

The local speeds of object contours vary systematically with the cosine of the angle between the normal component of the local velocity and the global object motion direction. An array of Gabor elements whose speed changes with local spatial orientation in accordance with this pattern can appear to move as a single surface. The apparent direction of motion of plaids and Gabor arrays has variously been proposed to result from feature tracking, vector addition and vector averaging in addition to the geometrically correct global velocity as indicated by the intersection of constraints (IOC) solution. Here a new combination rule, the harmonic vector average (HVA), is introduced, as well as a new algorithm for computing the IOC solution. The vector sum can be discounted as an integration strategy as it increases with the number of elements. The vector average over local vectors that vary in direction always provides an underestimate of the true global speed. The HVA, however, provides the correct global speed and direction for an unbiased sample of local velocities with respect to the global motion direction, as is the case for a simple closed contour. The HVA over biased samples provides an aggregate velocity estimate that can still be combined through an IOC computation to give an accurate estimate of the global velocity, which is not true of the vector average. Psychophysical results for type II Gabor arrays show perceived direction and speed falls close to the IOC direction for Gabor arrays having a wide range of orientations but the IOC prediction fails as the mean orientation shifts away from the global motion direction and the orientation range narrows. In this case perceived velocity generally defaults to the HVA.

Measuring ion temperatures and studying the ion energy balance in the high-latitude ionosphere

Data are presented for a nighttime ion heating event observed by the EISCAT radar on 16 December 1988. In the experiment, the aspect angle between the radar beam and the geomagnetic field was fixed at 54.7°, which avoids any ambiguity in derived ion temperature caused by anisotropy in the ion velocity distribution function. The data were analyzed with an algorithm which takes account of the non-Maxwellian line-of-sight ion velocity distribution. During the heating event, the derived spectral distortion parameter (D∗) indicated that the distribution function was highly distorted from a Maxwellian form when the ion drift increased to 4 km s−1. The true three-dimensional ion temperature was used in the simplified ion balance equation to compute the ion mass during the heating event. The ion composition was found to change from predominantly O4 to mainly molecular ions. A theoretical analysis of the ion composition, using the MSIS86 model and published values of the chemical rate coefficients, accounts for the order-of-magnitude increase in the atomic/molecular ion ratio during the event, but does not successfully explain the very high proportion of molecular ions that was observed.

A MODIS-Based Energy Balance to Estimate Evapotranspiration for Clear-Sky Days in Brazilian Tropical Savannas

Evapotranspiration (ET) plays an important role in global climate dynamics and in primary production of terrestrial ecosystems; it represents the mass and energy transfer from the land to atmosphere. Limitations to measuring ET at large scales using ground-based methods have motivated the development of satellite remote sensing techniques. The purpose of this work is to evaluate the accuracy of the SEBAL algorithm for estimating surface turbulent heat fluxes at regional scale, using 28 images from MODIS. SEBAL estimates are compared with eddy-covariance (EC) measurements and results from the hydrological model MGB-IPH. SEBAL instantaneous estimates of latent heat flux (LE) yielded r(2) = 0.64 and r(2) = 0.62 over sugarcane croplands and savannas when compared against in situ EC estimates. At the same sites, daily aggregated estimates of LE were r(2) = 0.76 and r(2) = 0.66, respectively. Energy balance closure showed that turbulent fluxes over sugarcane croplands were underestimated by 7% and 9% over savannas. Average daily ET from SEBAL is in close agreement with estimates from the hydrological model for an overlay of 38,100 km(2) (r(2) = 0.88). Inputs to which the algorithm is most sensitive are vegetation index (NDVI), gradient of temperature (dT) to compute sensible heat flux (H) and net radiation (Re). It was verified that SEBAL has a tendency to overestimate results both at local and regional scales probably because of low sensitivity to soil moisture and water stress. Nevertheless the results confirm the potential of the SEBAL algorithm, when used with MODIS images for estimating instantaneous LE and daily ET from large areas.

Flujo de potencia entre estructuras complejas sometidas a excitaciones de alta frecuencia y aplicaciones a la detección de daño estructural

El tema central de investigación en esta Tesis es el estudio del comportamientodinámico de una estructura mediante modelos que describen la distribución deenergía entre los componentes de la misma y la aplicación de estos modelos parala detección de daños incipientes.Los ensayos dinámicos son un modo de extraer información sobre las propiedadesde una estructura. Si tenemos un modelo de la estructura se podría ajustar éstepara que, con determinado grado de precisión, tenga la misma respuesta que elsistema real ensayado. Después de que se produjese un daño en la estructura,la respuesta al mismo ensayo variará en cierta medida; actualizando el modelo alas nuevas condiciones podemos detectar cambios en la configuración del modeloestructural que nos condujeran a la conclusión de que en la estructura se haproducido un daño.De este modo, la detección de un daño incipiente es posible si somos capacesde distinguir una pequeña variación en los parámetros que definen el modelo. Unrégimen muy apropiado para realizar este tipo de detección es a altas frecuencias,ya que la respuesta es muy dependiente de los pequeños detalles geométricos,dado que el tamaño característico en la estructura asociado a la respuesta esdirectamente proporcional a la velocidad de propagación de las ondas acústicas enel sólido, que para una estructura dada es inalterable, e inversamente proporcionala la frecuencia de la excitación. Al mismo tiempo, esta característica de la respuestaa altas frecuencias hace que un modelo de Elementos Finitos no sea aplicable enla práctica, debido al alto coste computacional.Un modelo ampliamente utilizado en el cálculo de la respuesta de estructurasa altas frecuencias en ingeniería es el SEA (Statistical Energy Analysis). El SEAaplica el balance energético a cada componente estructural, relacionando la energíade vibración de estos con la potencia disipada por cada uno de ellos y la potenciatransmitida entre ellos, cuya suma debe ser igual a la potencia inyectada a cadacomponente estructural. Esta relación es lineal y viene caracterizada por los factoresde pérdidas. Las magnitudes que intervienen en la respuesta se consideranpromediadas en la geometría, la frecuencia y el tiempo.Actualizar el modelo SEA a datos de ensayo es, por lo tanto, calcular losfactores de pérdidas que reproduzcan la respuesta obtenida en éste. Esta actualización,si se hace de manera directa, supone la resolución de un problema inversoque tiene la característica de estar mal condicionado. En la Tesis se propone actualizarel modelo SEA, no en término de los factores de pérdidas, sino en términos deparámetros estructurales que tienen sentido físico cuando se trata de la respuestaa altas frecuencias, como son los factores de disipación de cada componente, susdensidades modales y las rigideces características de los elementos de acoplamiento.Los factores de pérdidas se calculan como función de estos parámetros. Estaformulación es desarrollada de manera original en esta Tesis y principalmente sefunda en la hipótesis de alta densidad modal, es decir, que en la respuesta participanun gran número de modos de cada componente estructural.La teoría general del método SEA, establece que el modelo es válido bajounas hipótesis sobre la naturaleza de las excitaciones externas muy restrictivas,como que éstas deben ser de tipo ruido blanco local. Este tipo de carga es difícil dereproducir en condiciones de ensayo. En la Tesis mostramos con casos prácticos queesta restricción se puede relajar y, en particular, los resultados son suficientementebuenos cuando la estructura se somete a una carga armónica en escalón.Bajo estas aproximaciones se desarrolla un algoritmo de optimización por pasosque permite actualizar un modelo SEA a un ensayo transitorio cuando la carga esde tipo armónica en escalón. Este algoritmo actualiza el modelo no solamente parauna banda de frecuencia en particular sino para diversas bandas de frecuencia demanera simultánea, con el objetivo de plantear un problema mejor condicionado.Por último, se define un índice de daño que mide el cambio en la matriz depérdidas cuando se produce un daño estructural en una localización concreta deun componente. Se simula numéricamente la respuesta de una estructura formadapor vigas donde producimos un daño en la sección de una de ellas; como se tratade un cálculo a altas frecuencias, la simulación se hace mediante el Método delos Elementos Espectrales para lo que ha sido necesario desarrollar dentro de laTesis un elemento espectral de tipo viga dañada en una sección determinada. Losresultados obtenidos permiten localizar el componente estructural en que se haproducido el daño y la sección en que éste se encuentra con determinado grado deconfianza.AbstractThe main subject under research in this Thesis is the study of the dynamic behaviourof a structure using models that describe the energy distribution betweenthe components of the structure and the applicability of these models to incipientdamage detection.Dynamic tests are a way to extract information about the properties of astructure. If we have a model of the structure, it can be updated in order toreproduce the same response as in experimental tests, within a certain degree ofaccuracy. After damage occurs, the response will change to some extent; modelupdating to the new test conditions can help to detect changes in the structuralmodel leading to the conclusión that damage has occurred.In this way incipient damage detection is possible if we are able to detect srnallvariations in the model parameters. It turns out that the high frequency regimeis highly relevant for incipient damage detection, because the response is verysensitive to small structural geometric details. The characteristic length associatedwith the response is proportional to the propagation speed of acoustic waves insidethe solid, but inversely proportional to the excitation frequency. At the same time,this fact makes the application of a Finite Element Method impractical due to thehigh computational cost.A widely used model in engineering when dealing with the high frequencyresponse is SEA (Statistical Energy Analysis). SEA applies the energy balance toeach structural component, relating their vibrational energy with the dissipatedpower and the transmitted power between the different components; their summust be equal to the input power to each of them. This relationship is linear andcharacterized by loss factors. The magnitudes considered in the response shouldbe averaged in geometry, frequency and time.SEA model updating to test data is equivalent to calculating the loss factorsthat provide a better fit to the experimental response. This is formulated as an illconditionedinverse problem. In this Thesis a new updating algorithm is proposedfor the study of the high frequency response regime in terms of parameters withphysical meaning such as the internal dissipation factors, modal densities andcharacteristic coupling stiffness. The loss factors are then calculated from theseparameters. The approach is developed entirely in this Thesis and is mainlybased on a high modal density asumption, that is to say, a large number of modescontributes to the response.General SEA theory establishes the validity of the model under the asumptionof very restrictive external excitations. These should behave as a local white noise.This kind of excitation is difficult to reproduce in an experimental environment.In this Thesis we show that in practical cases this assumption can be relaxed, inparticular, results are good enough when the structure is excited with a harmonicstep function.Under these assumptions an optimization algorithm is developed for SEAmodel updating to a transient test when external loads are harmonic step functions.This algorithm considers the response not only in a single frequency band,but also for several of them simultaneously.A damage index is defined that measures the change in the loss factor matrixwhen a damage has occurred at a certain location in the structure. The structuresconsidered in this study are built with damaged beam elements; as we are dealingwith the high frequency response, the numerical simulation is implemented witha Spectral Element Method. It has therefore been necessary to develop a spectralbeam damaged element as well. The reported results show that damage detectionis possible with this algorithm, moreover, damage location is also possible withina certain degree of accuracy.

Energy and power aware scheduling algorithm modeling for battery powered embedded systems

Energy management has always been recognized as a challenge in mobile systems, especially in modern OS-based mobile systems where multi-functioning are widely supported. Nowadays, it is common for a mobile system user to run multiple applications simultaneously while having a target battery lifetime in mind for a specific application. Traditional OS-level power management (PM) policies make their best effort to save energy under performance constraint, but fail to guarantee a target lifetime, leaving the painful trading off between the total performance of applications and the target lifetime to the user itself. This thesis provides a new way to deal with the problem. It is advocated that a strong energy-aware PM scheme should first guarantee a user-specified battery lifetime to a target application by restricting the average power of those less important applications, and in addition to that, maximize the total performance of applications without harming the lifetime guarantee. As a support, energy, instead of CPU or transmission bandwidth, should be globally managed as the first-class resource by the OS. As the first-stage work of a complete PM scheme, this thesis presents the energy-based fair queuing scheduling, a novel class of energy-aware scheduling algorithms which, in combination with a mechanism of battery discharge rate restricting, systematically manage energy as the first-class resource with the objective of guaranteeing a user-specified battery lifetime for a target application in OS-based mobile systems. Energy-based fair queuing is a cross-application of the traditional fair queuing in the energy management domain. It assigns a power share to each task, and manages energy by proportionally serving energy to tasks according to their assigned power shares. The proportional energy use establishes proportional share of the system power among tasks, which guarantees a minimum power for each task and thus, avoids energy starvation on any task. Energy-based fair queuing treats all tasks equally as one type and supports periodical time-sensitive tasks by allocating each of them a share of system power that is adequate to meet the highest energy demand in all periods. However, an overly conservative power share is usually required to guarantee the meeting of all time constraints. To provide more effective and flexible support for various types of time-sensitive tasks in general purpose operating systems, an extra real-time friendly mechanism is introduced to combine priority-based scheduling into the energy-based fair queuing. Since a method is available to control the maximum time one time-sensitive task can run with priority, the power control and time-constraint meeting can be flexibly traded off. A SystemC-based test-bench is designed to assess the algorithms. Simulation results show the success of the energy-based fair queuing in achieving proportional energy use, time-constraint meeting, and a proper trading off between them. La gestión de energía en los sistema móviles está considerada hoy en día como un reto fundamental, notándose, especialmente, en aquellos terminales que utilizando un sistema operativo implementan múltiples funciones. Es común en los sistemas móviles actuales ejecutar simultaneamente diferentes aplicaciones y tener, para una de ellas, un objetivo de tiempo de uso de la batería. Tradicionalmente, las políticas de gestión de consumo de potencia de los sistemas operativos hacen lo que está en sus manos para ahorrar energía y satisfacer sus requisitos de prestaciones, pero no son capaces de proporcionar un objetivo de tiempo de utilización del sistema, dejando al usuario la difícil tarea de buscar un compromiso entre prestaciones y tiempo de utilización del sistema. Esta tesis, como contribución, proporciona una nueva manera de afrontar el problema. En ella se establece que un esquema de gestión de consumo de energía debería, en primer lugar, garantizar, para una aplicación dada, un tiempo mínimo de utilización de la batería que estuviera especificado por el usuario, restringiendo la potencia media consumida por las aplicaciones que se puedan considerar menos importantes y, en segundo lugar, maximizar las prestaciones globales sin comprometer la garantía de utilización de la batería. Como soporte de lo anterior, la energía, en lugar del tiempo de CPU o el ancho de banda, debería gestionarse globalmente por el sistema operativo como recurso de primera clase. Como primera fase en el desarrollo completo de un esquema de gestión de consumo, esta tesis presenta un algoritmo de planificación de encolado equitativo (fair queueing) basado en el consumo de energía, es decir, una nueva clase de algoritmos de planificación que, en combinación con mecanismos que restrinjan la tasa de descarga de una batería, gestionen de forma sistemática la energía como recurso de primera clase, con el objetivo de garantizar, para una aplicación dada, un tiempo de uso de la batería, definido por el usuario, en sistemas móviles empotrados. El encolado equitativo de energía es una extensión al dominio de la energía del encolado equitativo tradicional. Esta clase de algoritmos asigna una reserva de potencia a cada tarea y gestiona la energía sirviéndola de manera proporcional a su reserva. Este uso proporcional de la energía garantiza que cada tarea reciba una porción de potencia y evita que haya tareas que se vean privadas de recibir energía por otras con un comportamiento más ambicioso. Esta clase de algoritmos trata a todas las tareas por igual y puede planificar tareas periódicas en tiempo real asignando a cada una de ellas una reserva de potencia que es adecuada para proporcionar la mayor de las cantidades de energía demandadas por período. Sin embargo, es posible demostrar que sólo se consigue cumplir con los requisitos impuestos por todos los plazos temporales con reservas de potencia extremadamente conservadoras. En esta tesis, para proporcionar un soporte más flexible y eficiente para diferentes tipos de tareas de tiempo real junto con el resto de tareas, se combina un mecanismo de planificación basado en prioridades con el encolado equitativo basado en energía. En esta clase de algoritmos, gracias al método introducido, que controla el tiempo que se ejecuta con prioridad una tarea de tiempo real, se puede establecer un compromiso entre el cumplimiento de los requisitos de tiempo real y el consumo de potencia. Para evaluar los algoritmos, se ha diseñado en SystemC un banco de pruebas. Los resultados muestran que el algoritmo de encolado equitativo basado en el consumo de energía consigue el balance entre el uso proporcional a la energía reservada y el cumplimiento de los requisitos de tiempo real.

A mathematical framework for finite strain elastoplastic consolidation. Part 1: Balance laws, variational formulation, and linearization

A mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented. Strong and weak forms of the boundary-value problem are derived using both the material and spatial descriptions. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. Balance laws are written for the soil-water mixture following the motion of the soil matrix alone. It is shown that the motion of the fluid phase only affects the Jacobian of the solid phase motion, and therefore can be characterized completely by the motion of the soil matrix. Furthermore, it is shown from energy balance consideration that the effective, or intergranular, stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil-water mixture. Finally, it is shown that the mathematical model is amenable to consistent linearization, and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method.

Direct sequence spread spectrum based PWM strategy for harmonic reduction and communication

Switched mode power supplies (SMPSs) are essential components in many applications, and electromagnetic interference is an important consideration in the SMPS design. Spread spectrum based PWM strategies have been used in SMPS designs to reduce the switching harmonics. This paper proposes a novel method to integrate a communication function into spread spectrum based PWM strategy without extra hardware costs. Direct sequence spread spectrum (DSSS) and phase shift keying (PSK) data modulation are employed to the PWM of the SMPS, so that it has reduced switching harmonics and the input and output power line voltage ripples contain data. A data demodulation algorithm has been developed for receivers, and code division multiple access (CDMA) concept is employed as communication method for a system with multiple SMPSs. The proposed method has been implemented in both Buck and Boost converters. The experimental results validated the proposed DSSS based PWM strategy for both harmonic reduction and communication.

Customization of the design of antenna using genetic algorithm and finite-difference time-domain technique

Antenna design is an iterative process in which structures are analyzed and changed to comply with certain performance parameters required. The classic approach starts with analyzing a "known" structure, obtaining the value of its performance parameter and changing this structure until the "target" value is achieved. This process relies on having an initial structure, which follows some known or "intuitive" patterns already familiar to the designer. The purpose of this research was to develop a method of designing UWB antennas. What is new in this proposal is that the design process is reversed: the designer will start with the target performance parameter and obtain a structure as the result of the design process. This method provided a new way to replicate and optimize existing performance parameters. The base of the method was the use of a Genetic Algorithm (GA) adapted to the format of the chromosome that will be evaluated by the Electromagnetic (EM) solver. For the electromagnetic study we used XFDTD™ program, based in the Finite-Difference Time-Domain technique. The programming portion of the method was created under the MatLab environment, which serves as the interface for converting chromosomes, file formats and transferring of data between the XFDTD™ and GA. A high level of customization had to be written into the code to work with the specific files generated by the XFDTD™ program. Two types of cost functions were evaluated; the first one seeking broadband performance within the UWB band, and the second one searching for curve replication of a reference geometry. The performance of the method was evaluated considering the speed provided by the computer resources used. Balance between accuracy, data file size and speed of execution was achieved by defining parameters in the GA code as well as changing the internal parameters of the XFDTD™ projects. The results showed that the GA produced geometries that were analyzed by the XFDTD™ program and changed following the search criteria until reaching the target value of the cost function. Results also showed how the parameters can change the search criteria and influence the running of the code to provide a variety of geometries.

'Enhanced Direct and Indirect Genetic Algorithm Approaches for a Mall Layout and Tenant Selection Problem'

During our earlier research, it was recognised that in order to be successful with an indirect genetic algorithm approach using a decoder, the decoder has to strike a balance between being an optimiser in its own right and finding feasible solutions. Previously this balance was achieved manually. Here we extend this by presenting an automated approach where the genetic algorithm itself, simultaneously to solving the problem, sets weights to balance the components out. Subsequently we were able to solve a complex and non-linear scheduling problem better than with a standard direct genetic algorithm implementation.

Expedition in Data and Harmonic Analysis on Graphs

The graph Laplacian operator is widely studied in spectral graph theory largely due to its importance in modern data analysis. Recently, the Fourier transform and other time-frequency operators have been defined on graphs using Laplacian eigenvalues and eigenvectors. We extend these results and prove that the translation operator to the i’th node is invertible if and only if all eigenvectors are nonzero on the i’th node. Because of this dependency on the support of eigenvectors we study the characteristic set of Laplacian eigenvectors. We prove that the Fiedler vector of a planar graph cannot vanish on large neighborhoods and then explicitly construct a family of non-planar graphs that do exhibit this property. We then prove original results in modern analysis on graphs. We extend results on spectral graph wavelets to create vertex-dyanamic spectral graph wavelets whose support depends on both scale and translation parameters. We prove that Spielman’s Twice-Ramanujan graph sparsifying algorithm cannot outperform his conjectured optimal sparsification constant. Finally, we present numerical results on graph conditioning, in which edges of a graph are rescaled to best approximate the complete graph and reduce average commute time.

Enhanced Direct and Indirect Genetic Algorithm Approaches for a Mall Layout and Tenant Selection Problem

During our earlier research, it was recognised that in order to be successful with an indirect genetic algorithm approach using a decoder, the decoder has to strike a balance between being an optimiser in its own right and finding feasible solutions. Previously this balance was achieved manually. Here we extend this by presenting an automated approach where the genetic algorithm itself, simultaneously to solving the problem, sets weights to balance the components out. Subsequently we were able to solve a complex and non-linear scheduling problem better than with a standard direct genetic algorithm implementation.

'Enhanced Direct and Indirect Genetic Algorithm Approaches for a Mall Layout and Tenant Selection Problem'

During our earlier research, it was recognised that in order to be successful with an indirect genetic algorithm approach using a decoder, the decoder has to strike a balance between being an optimiser in its own right and finding feasible solutions. Previously this balance was achieved manually. Here we extend this by presenting an automated approach where the genetic algorithm itself, simultaneously to solving the problem, sets weights to balance the components out. Subsequently we were able to solve a complex and non-linear scheduling problem better than with a standard direct genetic algorithm implementation.

POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.

IMPACT OF PLUG-IN ELECTRIC VEHICLES AND WIND GENERATORS ON HARMONIC DISTORTION OF ELECTRIC DISTRIBUTION SYSTEMS

Harmonic distortion on voltages and currents increases with the increased penetration of Plug-in Electric Vehicle (PEV) loads in distribution systems. Wind Generators (WGs), which are source of harmonic currents, have some common harmonic profiles with PEVs. Thus, WGs can be utilized in careful ways to subside the effect of PEVs on harmonic distortion. This work studies the impact of PEVs on harmonic distortions and integration of WGs to reduce it. A decoupled harmonic three-phase unbalanced distribution system model is developed in OpenDSS, where PEVs and WGs are represented by harmonic current loads and sources respectively. The developed model is first used to solve harmonic power flow on IEEE 34-bus distribution system with low, moderate, and high penetration of PEVs, and its impact on current/voltage Total Harmonic Distortions (THDs) is studied. This study shows that the voltage and current THDs could be increased upto 9.5% and 50% respectively, in case of distribution systems with high PEV penetration and these THD values are significantly larger than the limits prescribed by the IEEE standards. Next, carefully sized WGs are selected at different locations in the 34-bus distribution system to demonstrate reduction in the current/voltage THDs. In this work, a framework is also developed to find optimal size of WGs to reduce THDs below prescribed operational limits in distribution circuits with PEV loads. The optimization framework is implemented in MATLAB using Genetic Algorithm, which is interfaced with the harmonic power flow model developed in OpenDSS. The developed framework is used to find optimal size of WGs on the 34-bus distribution system with low, moderate, and high penetration of PEVs, with an objective to reduce voltage/current THD deviations throughout the distribution circuits. With the optimal size of WGs in distribution systems with PEV loads, the current and voltage THDs are reduced below 5% and 7% respectively, which are within the limits prescribed by IEEE.