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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
241

Computational tools for soft sensing and state estimation

Balakrishnapillai Chitralekha, Saneej 06 1900 (has links)
The development of fast and efficient computer hardware technology has resulted in the rapid development of numerous computational software tools for making statistical inferences. The computational algorithms, which are the backbone of these tools, originate from distinct areas in science, mathematics and engineering. The main focus of this thesis is on computational tools which can be employed for estimating unmeasured variables in a process using all the available prior information. Specifically, this thesis demonstrates the application of a variety of tools for soft sensing of process variables and uncertain parameters of physiochemical process models, using routine data available from the process. The application examples presented in this thesis come from broad areas where process uncertainty is inherent and includes petrochemical processes, mechanical valve actuators, and upstream production processes in petroleum reservoirs. The mathematical models that are employed in different domains vary significantly in their structure and their level of complexity. In the petrochemical domain, the focus was on developing empirical soft sensors which are essentially nonparametric mathematical models identified using routine data from the process. The Support Vector Regression technique was applied for identifying such nonparametric empirical models. On the other hand, in all the other application examples in this thesis the physical parametric models of the process were utilized. The latter application examples, which cover a major portion of this thesis, demonstrate the application of modern state and parameter estimation algorithms which are firmly grounded on Bayesian theory and Monte Carlo techniques. Prior to the chapters on the application of state and parameter estimation techniques, a tutorial overview of the Monte Carlo simulation based state estimation algorithms is provided with an attempt to throw new light on these techniques. The tutorial is aimed at making these techniques simple to visualize and understand. The application case studies serve to illustrate the performance of the different algorithms. All case studies presented in this thesis are performed on processes that exhibit significant nonlinearity in terms of the relationship between the process input variables and output variables. / Process Control
242

A state estimation framework for ultrasonic structural health monitoring of fastener hole fatigue cracks

Cobb, Adam 10 March 2008 (has links)
The development of structural monitoring systems is a critical research area because of the age and sustainment costs associated with many aircraft in use today. Specifically, integrated structural health monitoring (SHM) systems are advantageous because they allow for automated, near real-time assessment of the state of the structure, where the automation improves both the accuracy of the measurements and allows for more frequent system interrogation than possible with traditional nondestructive evaluation methods. Ultrasonic techniques are particularly well-suited for SHM systems because of their potential to detect and track damage well before structural failure using in situ sensors. The research problem considered in this thesis is detection and tracking of fatigue cracks emanating from fastener holes in metallic structural components. The sensing method utilizes attached ultrasonic transducers, and tracking of damage is achieved by employing a state estimation framework that incorporates a well-known empirical model for crack growth and a measurement model relating the ultrasonic response to crack size. The state estimation process is preceded by an automated crack detection algorithm, and can be followed by a prediction of remaining life assuming future usage. The state estimation framework provides a better estimate of crack size than either the ultrasonic measurement model or crack growth model alone. Although the example application is monitoring of fastener holes, the general approach is applicable to a variety of SHM problems.
243

Robust nonlinear observer for a non-collocated flexible motion system

Waqar, Mohsin 01 April 2008 (has links)
Robustness of the closed-loop system has repercussions on both stability and performance, making the study of robustness very important. Fundamentally, the performance and stability of closed-loop systems utilizing state-feedback are tied to that of the observers. The primary goal of this thesis is to develop a robust nonlinear observer and closely examine the usefulness of the observer in the presence of non-collocation and parametric uncertainty and as an integral component in closed-loop control. The usefulness of the observer being investigated depends on robustness, accuracy, computational burden, tunability, ease of design, and ease of implementation on an actual flexible motion system. The design and subsequent integration of the Kalman filter, an optimal observer, into a closed-loop system is well known and systematic. However, there are shortcomings of the Kalman filter in the presence of model uncertainty which are highlighted in this work. Simulation studies are conducted using the Simulation Module in National Instruments LabVIEW 8.5 and experiments are conducted on a physical system consisting of a single flexible link with non-collocation of actuators and sensors using LabVIEW Real Time 8.5. Simulations serve as a means to analyze the performance of the optimal observer and the robust observer by analyzing their dynamic behavior as well as that of the closed-loop system with each observer in place. The focus of experiments is on investigating implementation of the robust observer, including initialization and tuning of observer design parameters off-line and on-line. Simulations verify the robustness properties of the sliding mode observer while experiments show that the robust observer can be implemented at fast control rates and that replacing the Kalman filter with a robust observer has direct ramifications on closed-loop performance.
244

Robust adaptive control of rigid spacecraft attitude maneuvers

Dando, Aaron John January 2008 (has links)
In this thesis novel feedback attitude control algorithms and attitude estimation algorithms are developed for a three-axis stabilised spacecraft attitude control system. The spacecraft models considered include a rigid-body spacecraft equipped with (i) external control torque devices, and (ii) a redundant reaction wheel configuration. The attitude sensor suite comprises a three-axis magnetometer and three-axis rate gyroscope assembly. The quaternion parameters (also called Euler symmetric parameters), which globally avoid singularities but are subject to a unity-norm constraint, are selected as the primary attitude coordinates. There are four novel contributions presented in this thesis. The first novel contribution is the development of a robust control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix, actuator magnitude constraints, bounded persistent external disturbances, and state estimation error. The novel component of this algorithm is the incorporation of state estimation error into the stability analysis. The proposed control law contains a parameter which is dynamically adjusted to ensure global asymptotic stability of the overall closedloop system, in the presence of these specific system non-idealities. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The control design approach also ensures minimum angular path maneuvers, since the attitude quaternion parameters are not unique. The second novel contribution is the development of a robust direct adaptive control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix. The novel aspect of this algorithm is the incorporation of a composite parameter update strategy, which ensures global exponential convergence of the closed-loop system. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The exponential convergence results provided by this control strategy require persistently exciting reference trajectory commands. The control design approach also ensures minimum angular path maneuvers. The third novel contribution is the development of an optimal control strategy for spacecraft attitude maneuvers, based on a rigid body spacecraft model including a redundant reaction wheel assembly. The novel component of this strategy is the proposal of a performance index which represents the total electrical energy consumed by the reaction wheel over the maneuver interval. Pontraygin's minimum principle is applied to formulate the necessary conditions for optimality, in which the control torques are subject to timevarying magnitude constraints. The presence of singular sub-arcs in the statespace and their associated singular controls are investigated using Kelley's necessary condition. The two-point boundary-value problem (TPBVP) is formulated using Pontrayagin's minimum principle. The fourth novel contribution is an attitude estimation algorithm which estimates the spacecraft attitude parameters and sensor bias parameters from three-axis magnetometer and three-axis rate gyroscope measurement data. The novel aspect of this algorithm is the assumption that the state filtering probability density function (PDF) is Gaussian distributed. This Gaussian PDF assumption is also applied to the magnetometer measurement model. Propagation of the filtering PDF between sensor measurements is performed using the Fokker-Planck equation, and Bayes theorem incorporates measurement update information. The use of direction cosine matrix elements as the attitude coordinates avoids any singularity issues associated with the measurement update and estimation error covariance representation.
245

State and parameter estimation of physics-based lithium-ion battery models

Bizeray, Adrien January 2016 (has links)
This thesis investigates novel algorithms for enabling the use of first-principle electrochemical models for battery monitoring and control in advanced battery management systems (BMSs). Specifically, the fast solution and state estimation of a high-fidelity spatially resolved thermal-electrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional (P2D) model are investigated. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This implementation of the P2D model is then used in combination with an extended Kalman filter (EKF) algorithm modified for differential-algebraic equations (DAEs) to estimate the states of the model, e.g. lithium concentrations, overpotential. The state estimation algorithm is able to rapidly recover the model states from current, voltage and temperature measurements. Results show that the error on the state estimate falls below 1% in less than 200s despite a 30% error on battery initial state-of-charge (SoC) and additive measurement noise with 10mV and 0.5°C standard deviations. The parameter accuracy of such first-principle models is of utmost importance for the trustworthy estimation of internal battery electrochemical states. Therefore, the identifiability of the simpler single particle (SP) electrochemical model is investigated both in principle and in practice. Grouping parameters and partially non-dimensionalising the SP model equations in order to understand the maximum expected degrees of freedom in the problem reveals that there are only six unique parameters in the SP model. The structural identifiability is then examined by asking whether the transfer function of the linearised SP model is unique. It is found that the model is unique provided that the electrode open circuit voltage curves have a non-zero gradient, the parameters are ordered, and that the behaviour of the kinetics of each electrode is lumped together into a single parameter which is the charge transfer resistance. The practical estimation of the SP model parameters from frequency-domain experimental data obtained by electrochemical impedance spectroscopy (EIS) is then investigated and shows that estimation at a single SoC is insufficient to obtain satisfactory results and EIS data at multiple SoCs must be combined.
246

An adaptive multi-agent system for the distribution of intelligence in electrical distribution networks : state estimation / Un système multi-agent auto-adaptatif pour la distribution de l'intelligence dans les réseaux électriques de distribution : estimation d'état

Perles, Alexandre 09 February 2017 (has links)
L'électricité joue un rôle de plus en plus important dans notre société. En effet, nous nous dirigeons vers l'ère du "tout électrique". Les besoins évoluant, il est indispensable de repenser la manière dont l'électricité est produite et distribuée. Cela introduit le concept de Smart Grid. Le Smart Grid est un concept de réseau électrique capable de supporter de manière autonome et intelligente les changements et pannes qui pourraient survenir dans un réseau. Cela répond directement au fait que de part la nature fortement distribuée et l'imprédictibilité de l'environnement (météo, ...), ces événements sont imprévisibles. Pour cela, cette thèse propose un cadre applicatif (framework) innovant basé sur les multi-agents ainsi que la conception et l'implémentation de comportements coopératifs pour résoudre deux problémes courants dans les réseaux électriques: l'analyse des flux de puissance et l'estimation d'état. Ces problèmes ont été abordés avec l'approche des Systèmes Multi-Agent Adaptatifs. Ces systèmes sont efficaces pour résoudre des problèmes complexes et ont la capacité d'adapter leur fonctionnement aux évolutions de leur environnement. Les résultats obtenus indiquent la pertinence d'utiliser de tels systèmes adaptatifs pour résoudre les problèmes inhérents au concept de Smart Grid. / Electricity plays an increasingly important role in our society. Indeed, we are moving toward the era of "everything electric". The needs evolving, it is mandatory to rethink the way electricity is produced and distributed. This then introduces the concept of an autonomous and intelligent power system called the Smart Grid. The Smart Grid is a concept of electrical network able to support autonomously any changes and faults that may occur. Obviously, the geographical distribution of electrical networks and the environment (weather conditions, ...) make it impossible to predict events that will occur. To do this, this study proposes an innovative agent-based framework as well as the design and implementation of cooperative agents behaviors aiming at solving common power systems related problems: the Load Flow analysis and the State Estimation. These issues have been addressed by the mean of Adaptive Multi-Agent Systems. These systems are known to be efficient to solve complex problems and have the ability to adapt their functioning to the evolutions of their environment. The results obtained show the relevance of using such self-adaptive systems to solve the issues inherent to the Smart Grid.
247

Novos métodos de estimação de estado multi-área com potencial aplicação em redes elétricas inteligentes / New methods for multi-area state estimation with potential application in the smart grid

Milbradt, Rafael Gressler 06 March 2015 (has links)
The smart grid will enable a revolution in the way we manage and relates to the distribution networks through intelligent applications. For many of these applications, it is understood that one of the primary activities to provide real time operation is to be aware of the electric state of the network by monitoring and using remote measurements. This thesis addresses the topic of state estimation proposing the use of methods that best fit the requirements of smart distribution networks. In a first moment it is understood that the monitoring will not be satisfactorily comprehensive, and then there will need to merge real measures with not real measures obtained through historical data and direct methods such as calculating the power flow. Another important requirement of these methods is to combine great complexity and large number of buses of the distribution network to a satisfactory response time that allows real-time monitoring. Thus this thesis uses an approach that enables multiprocessing of algorithms like Power Flow and State Estimation in order to get faster response times in multiprocessor environments, which now are quite common. In the case of State Estimator has been proposed a Multi-area estimator associated to an algorithm for massive division of the networks which allows to drastically reduce the complexity of the algorithm without compromising the accuracy of the estimator solution. Nevertheless, other concepts related to state estimation, but adapted to the context of smart grids are also addressed as the detection of errors in measurements, topology errors and to the ideal location of meters, which may have important influence on the accuracy of the obtained result. The ASW software - Analysis of Distribution Systems Web was developed to implement the proposed methodologies. The software is a totally working prototype, already tested on a real distribution networks and have demonstrated good results and potential for managing a distribution system in an smart way. / As redes elétricas inteligentes permitirão uma revolução na forma como se gerencia e se relaciona com as redes de distribuição, através de aplicações inteligentes. Para diversas destas aplicações, entende-se que uma das atividades primordiais para proporcionar a operação em tempo real é ter conhecimento do estado elétrico da rede através do monitoramento e do uso de medidas remotas. A presente tese aborda o tema de estimação de estado propondo o uso de métodos que melhor se adaptam aos requisitos das redes de distribuição inteligentes. Num primeiro momento entende-se que o monitoramento não será satisfatoriamente abrangente, então haverá a necessidade de mesclar medidas remotas reais com outras pseudo-medidas obtidas através de dados históricos e métodos diretos como o cálculo do Fluxo de Potência. Outro requisito importante destes métodos é conseguir conciliar a grande complexidade e o elevado número de nós das redes de distribuição a um tempo de resposta satisfatório que permita o monitoramento em tempo real. Desta forma a presente tese utiliza uma abordagem que permite o multiprocessamento dos algoritmos de Fluxo de Potência e Estimação de Estado de forma a obter um menor tempo de resposta em ambientes multiprocessados, que são bastante comuns atualmente. No caso do Estimador de Estados, foi proposto um estimador multi-área associado a um algoritmo de divisão maciça das redes, que permite reduzir drasticamente a complexidade do algoritmo sem comprometer a precisão da solução. Todavia, outros conceitos relacionados à estimação de estado, porém adaptados ao contexto de redes de distribuição inteligentes também são abordados como a detecção de erros em medidas, erros de topologia e a localização ideal de medidores, os quais podem ter importante influência na precisão do resultado obtido. O software ASW Análise de Sistemas de Distribuição Web foi desenvolvido para implementação das metodologias propostas. O Software ainda se encontra sob a forma de um protótipo, contudo já se apresenta funcional em redes de distribuição reais e demonstrando bons resultados e potencialidades para o gerenciamento de um sistema de distribuição inteligente.
248

A Multi-Sensor Data Fusion Approach for Real-Time Lane-Based Traffic Estimation

January 2015 (has links)
abstract: Modern intelligent transportation systems (ITS) make driving more efficient, easier, and safer. Knowledge of real-time traffic conditions is a critical input for operating ITS. Real-time freeway traffic state estimation approaches have been used to quantify traffic conditions given limited amount of data collected by traffic sensors. Currently, almost all real-time estimation methods have been developed for estimating laterally aggregated traffic conditions in a roadway segment using link-based models which assume homogeneous conditions across multiple lanes. However, with new advances and applications of ITS, knowledge of lane-based traffic conditions is becoming important, where the traffic condition differences among lanes are recognized. In addition, most of the current real-time freeway traffic estimators consider only data from loop detectors. This dissertation develops a bi-level data fusion approach using heterogeneous multi-sensor measurements to estimate real-time lane-based freeway traffic conditions, which integrates a link-level model-based estimator and a lane-level data-driven estimator. Macroscopic traffic flow models describe the evolution of aggregated traffic characteristics over time and space, which are required by model-based traffic estimation approaches. Since current first-order Lagrangian macroscopic traffic flow model has some unrealistic implicit assumptions (e.g., infinite acceleration), a second-order Lagrangian macroscopic traffic flow model has been developed by incorporating drivers’ anticipation and reaction delay. A multi-sensor extended Kalman filter (MEKF) algorithm has been developed to combine heterogeneous measurements from multiple sources. A MEKF-based traffic estimator, explicitly using the developed second-order traffic flow model and measurements from loop detectors as well as GPS trajectories for given fractions of vehicles, has been proposed which gives real-time link-level traffic estimates in the bi-level estimation system. The lane-level estimation in the bi-level data fusion system uses the link-level estimates as priors and adopts a data-driven approach to obtain lane-based estimates, where now heterogeneous multi-sensor measurements are combined using parallel spatial-temporal filters. Experimental analysis shows that the second-order model can more realistically reproduce real world traffic flow patterns (e.g., stop-and-go waves). The MEKF-based link-level estimator exhibits more accurate results than the estimator that uses only a single data source. Evaluation of the lane-level estimator demonstrates that the proposed new bi-level multi-sensor data fusion system can provide very good estimates of real-time lane-based traffic conditions. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2015
249

Contextual information aided target tracking and path planning for autonomous ground vehicles

Ding, Runxiao January 2016 (has links)
Recently, autonomous vehicles have received worldwide attentions from academic research, automotive industry and the general public. In order to achieve a higher level of automation, one of the most fundamental requirements of autonomous vehicles is the capability to respond to internal and external changes in a safe, timely and appropriate manner. Situational awareness and decision making are two crucial enabling technologies for safe operation of autonomous vehicles. This thesis presents a solution for improving the automation level of autonomous vehicles in both situational awareness and decision making aspects by utilising additional domain knowledge such as constraints and influence on a moving object caused by environment and interaction between different moving objects. This includes two specific sub-systems, model based target tracking in environmental perception module and motion planning in path planning module. In the first part, a rigorous Bayesian framework is developed for pooling road constraint information and sensor measurement data of a ground vehicle to provide better situational awareness. Consequently, a new multiple targets tracking (MTT) strategy is proposed for solving target tracking problems with nonlinear dynamic systems and additional state constraints. Besides road constraint information, a vehicle movement is generally affected by its surrounding environment known as interaction information. A novel dynamic modelling approach is then proposed by considering the interaction information as virtual force which is constructed by involving the target state, desired dynamics and interaction information. The proposed modelling approach is then accommodated in the proposed MTT strategy for incorporating different types of domain knowledge in a comprehensive manner. In the second part, a new path planning strategy for autonomous vehicles operating in partially known dynamic environment is suggested. The proposed MTT technique is utilized to provide accurate on-board tracking information with associated level of uncertainty. Based on the tracking information, a path planning strategy is developed to generate collision free paths by not only predicting the future states of the moving objects but also taking into account the propagation of the associated estimation uncertainty within a given horizon. To cope with a dynamic and uncertain road environment, the strategy is implemented in a receding horizon fashion.
250

Um algoritmo para estima??o de estado em alimentadores de distribui??o de energia el?trica com base no m?todo da soma de pot?ncias

Almeida, Marcos Antonio Dias de 29 December 2003 (has links)
Made available in DSpace on 2014-12-17T14:55:01Z (GMT). No. of bitstreams: 1 MarcosADA.pdf: 1444489 bytes, checksum: 289536fadcf88cdfafb2eefa6b4f2ac4 (MD5) Previous issue date: 2003-12-29 / Most algorithms for state estimation based on the classical model are just adequate for use in transmission networks. Few algorithms were developed specifically for distribution systems, probably because of the little amount of data available in real time. Most overhead feeders possess just current and voltage measurements at the middle voltage bus-bar at the substation. In this way, classical algorithms are of difficult implementation, even considering off-line acquired data as pseudo-measurements. However, the necessity of automating the operation of distribution networks, mainly in regard to the selectivity of protection systems, as well to implement possibilities of load transfer maneuvers, is changing the network planning policy. In this way, some equipments incorporating telemetry and command modules have been installed in order to improve operational features, and so increasing the amount of measurement data available in real-time in the System Operation Center (SOC). This encourages the development of a state estimator model, involving real-time information and pseudo-measurements of loads, that are built from typical power factors and utilization factors (demand factors) of distribution transformers. This work reports about the development of a new state estimation method, specific for radial distribution systems. The main algorithm of the method is based on the power summation load flow. The estimation is carried out piecewise, section by section of the feeder, going from the substation to the terminal nodes. For each section, a measurement model is built, resulting in a nonlinear overdetermined equations set, whose solution is achieved by the Gaussian normal equation. The estimated variables of a section are used as pseudo-measurements for the next section. In general, a measurement set for a generic section consists of pseudo-measurements of power flows and nodal voltages obtained from the previous section or measurements in real-time, if they exist -, besides pseudomeasurements of injected powers for the power summations, whose functions are the load flow equations, assuming that the network can be represented by its single-phase equivalent. The great advantage of the algorithm is its simplicity and low computational effort. Moreover, the algorithm is very efficient, in regard to the accuracy of the estimated values. Besides the power summation state estimator, this work shows how other algorithms could be adapted to provide state estimation of middle voltage substations and networks, namely Schweppes method and an algorithm based on current proportionality, that is usually adopted for network planning tasks. Both estimators were implemented not only as alternatives for the proposed method, but also looking for getting results that give support for its validation. Once in most cases no power measurement is performed at beginning of the feeder and this is required for implementing the power summation estimations method, a new algorithm for estimating the network variables at the middle voltage bus-bar was also developed / A grande maioria dos algoritmos de estima??o de estado, que usa o modelo cl?ssico, se destina ? aplica??o em sistemas de transmiss?o. H? poucos algoritmos para sistemas de distribui??o. Isto se deve em parte, a pequena quantidade de dados de medi??o dispon?veis em tempo real. A maioria dos alimentadores s? disp?e de medi??o de corrente na sa?da do barramento de m?dia tens?o da subesta??o. Dessa forma, a aplica??o de algoritmos tradicionais de estima??o de estado para a supervis?o de alimentadores pode ser inadequada, mesmo considerando dados obtidos off-line atrav?s de pseudomedi??es. Entretanto, a necessidade de automatiza??o da opera??o dos sistemas de distribui??o, principalmente no que diz respeito ? seletividade quando da presen?a de defeitos, fez surgir alguns equipamentos telecomandados, que incorporam m?dulos de telemedi??o de algumas grandezas da rede, que podem ser transmitidas em tempo real para o centro de opera??o do sistema COS. Isso permite o desenvolvimento de um novo modelo de estimador de estado, envolvendo medidas reais e pseudomedidas de cargas, que s?o constru?das a partir da defini??o de fatores de pot?ncia e de utiliza??o t?picos de sistemas de distribui??o. O presente trabalho trata do desenvolvimento de um novo modelo de estimador de estado voltado para sistemas de distribui??o, particularmente, alimentadores radiais. Baseia-se no algoritmo do fluxo de carga soma de pot?ncias. Da? o nome estimador de estado de soma de pot?ncias. O m?todo faz a estima??o de alimentador por se??o, partindo da subesta??o para os ramais. Para cada se??o ? constru?do o modelo de medi??o. Isto resulta em sistemas de equa??es n?o-lineares, sobre determinados, que requerem uma solu??o iterativa. Obt?m-se essa solu??o atrav?s do m?todo dos m?nimos quadrados ponderados via equa??o normal de Gauss. As grandezas estimadas em uma se??o s?o usadas como pseudomedidas para estimar a se??o subseq?ente. O conjunto de medi??o de cada se??o ? constitu?do por pseudomedidas ou medidas de fluxos de pot?ncia nos trechos e tens?es nodais, em tempo real, e por pseudomedidas de inje??es de pot?ncias nos n?s. As pseudomedidas de inje??es de pot?ncia s?o constru?das a partir das equa??es cl?ssicas de pot?ncias injetadas, usadas no estudo de fluxo de carga. Assume-se ainda, que o sistema trif?sico pode ser representado por seu equivalente monof?sico. A grande vantagem do algoritmo est? na simplicidade e rapidez do programa computacional que o implementa. Al?m disso, ? muito eficiente no que diz respeito ? exatid?o das grandezas estimadas. Al?m do estimador soma de pot?ncias, este trabalho mostra como outros algoritmos poderiam ser adaptados para prover estima??o de estado de subesta??es e circuitos de m?dia tens?o, isto ?, o m?todo de Schweppe e um algoritmo baseado em proporcionalidade de corrente, que normalmente ? usado em estudos de planejamento de redes. Ambos os estimadores foram implementados n?o somente como alternativas para o m?todo proposto, mas tamb?m procurando obter resultados para servir de suporte para sua valida??o. Uma vez que na maioria dos casos n?o h? medi??o de pot?ncias na sa?da para o alimentador e esta ? requerida para implementa??o do m?todo da soma de pot?ncias, um novo algoritmo para estimar as grandezas de rede em barra de m?dia tens?o foi tamb?m desenvolvido

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