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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.
11

Otimização de linhas de transmissão para manobra de abertura monopolar - análise da influência dos parâmetros transversais do sistema de compensação reativa / Optimization of transmission lines to single-phase opening maneuver - analysis of the influence of transversal parameters of shunt reactive compensation system

Zevallos Alcahuaman, Milton Elvis, 1974- 03 January 2013 (has links)
Orientador: Maria Cristina Dias Tavares / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-25T04:28:30Z (GMT). No. of bitstreams: 1 ZevallosAlcahuaman_MiltonElvis_D.pdf: 2479285 bytes, checksum: 4c1c5f42e8da1a073caee7cb88308479 (MD5) Previous issue date: 2013 / Resumo: Uma solução bastante utilizada para reduzir a corrente de arco secundário nas linhas aéreas de transmissão em extra-alta-tensão após a ocorrência de faltas monofásicas não permanentes é a inserção de um reator de neutro no arranjo dos reatores dos bancos de compensação reativa em derivação da linha. Muitas vezes estes reatores de neutro não são otimizados, de modo que reatores com valores típicos são especificados nos projetos de linhas de transmissão aéreas, baseados simplesmente no seu nível de tensão, mas sem considerar as especificidades das linhas, como as suas características físicas ou o seu comprimento. A especificação inadequada do reator de neutro pode resultar em correntes de arco secundário elevadas, o que, em última análise, pode reduzir a taxa de sucesso da manobra de religamento monopolar. Além disto, o custo do sistema de compensação pode ser maior do que o necessário. A tese apresenta uma extensa análise de sensibilidade dos principais parâmetros que influenciam no dimensionamento de um tronco de transmissão longo, especificamente do nível de compensação mais adequado e do valor ótimo do reator de neutro. Destaca-se na pesquisa o desenvolvimento de uma representação dos componentes de um sistema de transmissão através de quadripolos trifásicos com o intuito de obter a resposta sustentada durante o desequilíbrio. Através desta representação foi possível identificar a relação entre o reator de neutro ótimo e os parâmetros transversais da linha de transmissão, assim como a influência direta entre o nível de compensação do sistema com o valor do reator de neutro otimizado. Adicionalmente foram identificados comprimentos limites para linhas não compensadas de diferentes níveis de tensão de modo a ainda apresentar alta probabilidade de sucesso para a manobra monopolar. Simulações de faltas monofásicas foram realizadas utilizando dados provenientes de linhas típicas do sistema elétrico brasileiro / Abstract: A widely used solution to reduce secondary arc current in the overhead transmission lines in EHV after single-phase non permanents faults is the insertion of a neutral reactor in the arrangement forming part of the shunt reactive compensation of the line. Frequently in Brazilian electrical system, neutral reactors are not optimized, so that reactors with typical values are specified in the project of overhead transmission lines based on their voltage level, but without considering the specifics line parameters, as their physical characteristics or their length. The specification of unsuitable neutral reactor can result in high secondary arc currents, which eventually diminishes the success rate of single-phase automatic reclosure (SPAR) maneuver. Moreover, the cost of the compensation system may be larger than necessary. This paper presents an extensive sensitivity analysis of the main parameters that influence the project of a long transmission trunk, specifically the most appropriate level of compensation and the optimal value of the neutral reactor. It is noteworthy the development of a transmission system components representation using three-phase two-ports networks in order to obtain sustained response during unbalance. Through this analysis it was possible to identify the relationship between the shunt reactor and the optimized neutral parameter and the influence of the compensation level with the neutral reactor optimized value. Additionally the maximum lengths of non-compensated lines that would have high probability of success of SPAR maneuver were identified. Simulations of single-phase faults were performed using data from typical lines of the Brazilian electric system / Doutorado / Energia Eletrica / Doutor em Engenharia Elétrica
12

Falhas em linhas de transmissão elétrica na região sudeste do Brasil e efeitos do ambiente geofísico / Power transmission failures in southeastern Brazil and the effects geophysical environment

Duro, Magda Aparecida Salgueiro, 1968- 06 November 2013 (has links)
Orientadores: José Pissolato Filho, Pierre Kaufmann / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-23T01:41:59Z (GMT). No. of bitstreams: 1 Duro_MagdaAparecidaSalgueiro_D.pdf: 3861523 bytes, checksum: f5896319d2a3653a7903f977210f3ac1 (MD5) Previous issue date: 2013 / Resumo: A atual dependência da sociedade aos diversos sistemas tecnológicos em funcionamento na Terra traz uma constante preocupação pela sua vulnerabilidade a fatores menos conhecidos. As possíveis falhas no fornecimento de energia elétrica podem ocasionar transtornos de grande impacto às comunidades podendo acarretar perdas financeiras expressivas. Diversos fatores podem ocasionar falhas nas linhas de transmissão, entre eles, os fatores climáticos. Nesse contexto, são pouco conhecidas as influências qualitativas de distintos fatores, destacando-se os efeitos do denominado clima espacial. Há indicações que o clima espacial influencia a alta atmosfera terrestre, com repercussão no clima bem como em sistemas de engenharia em operação na Terra. As redes de transmissão de alta tensão representam um grande circuito elétrico pouco acima do solo sujeito a uma série de sobrecargas temporárias de vários tipos, algumas das quais podem levar a falhas. Algumas destas falhas podem estar relacionadas ao ambiente geofísico. Neste trabalho foi analisada uma base de dados sem precedentes de falhas em linhas de transmissão por um longo período (nove anos) numa grande malha localizada no Estado de São Paulo (sudeste do Brasil). O período estudado (1998-2006) compreende uma significativa fração do ciclo de atividade solar 23. A concessionária responsável (ISA.CTEEP) pela operação das linhas estudadas classifica as falhas em noventa e cinco tipos distintos de causas possíveis, sendo que a maior parte está relacionada às descargas atmosféricas. Este estudo está relacionado aos desligamentos devido às descargas atmosféricas, em duas redes de alta voltagem da companhia, de 138 kV e de 440 kV. No período estudado, estes desligamentos correspondem a 1.957 (42,80%) num total de 4.572 para a linha de 138 kV e de 170 (22,28%) sobre 763 para a linha de 440 kV. Equivale a menos de um a cada dez mil do número total de descargas atmosféricas ocorridas na mesma área, o que demonstra alta resiliência das redes de potência em relação aos raios. Durante a época das chuvas, há uma maior concentração de desligamentos. Para todo o período estudado houve redução de 67% e 77% no número de desligamentos devido às descargas atmosféricas, para as linhas de 138 kV e 440 kV, respectivamente, havendo uma boa correspondência com a redução do número de manchas solares. Nenhuma correlação foi encontrada em relação às atividades geomagnéticas caracterizadas pelo índice planetário (Kp) e pelas grandes tempestades (Dst) tanto em longos quanto em curtos prazos. Uma explicação sugerida associa a diminuição da atividade solar ao aumento da condutividade na atmosfera causada pelo maior fluxo de raios cósmicos. Consequentemente poderá ocorrer uma redução do limiar de voltagem necessário para produzir descargas atmosféricas para provocar desligamentos nas redes de alta voltagem. O circuito elétrico global descrito pelo acoplamento ionosfera-terra (a eletrosfera) exerce um papel importante para explicar a redução dos desligamentos. Com o aumento da condutividade atmosférica as descargas são menos potentes, resultando em menor número de desligamentos com o decréscimo do ciclo solar / Abstract: The current society dependence on the operating technological systems on the Earth brings a permanent concern for their vulnerability to not well known factors. Possible failures in electricity supply can cause inconveniences with large impact to the communities, which may cause significant financial losses. Different factors can cause failures in the transmission networks, including, climate factors. In this context, the influences of various qualitative factors, especially the effects of space weather are not well known. There are indications that space weather affects the upper atmosphere, with repercussions on the climate as well as in engineering systems in operation on Earth. High-voltage transmission networks represent large electrical circuits just above the ground which are subjected to a number of transient overcharges of various kinds, some of which may lead to failures. Some failures might be related to anomalies of the geophysical environment. In the present study we analyze a database consisting in a one unprecedented long series of transmission grid failures (nine years) on high-voltage networks located in São Paulo state (southeastern Brazil). The studied period (1998-2006) includes an important fraction of the solar activity cycle 23. The company responsible by the power grid operator (ISA.CTEEP) classifies causes in ninety-five distinct failure classes to explain the transmission grid shut downs. Most of the failures were attributed to atmospheric discharges. We have studied the failures attributed to atmospheric discharge, in the two power grids of the company, 138 kV and 440 kV. The failures attributed to atmospheric discharge correspond to 1.957 (42.80%) for a total 4.572 at 138 kV and to 170 (22.8%) out of 763 at 440 kV. They correspond to less than one ten thousandth of the actual number of atmospheric discharges recorded in the same area, demonstrating the grid's high resilience to breakdowns due to lightning. A clear concentration of failures in the region's thunderstorm season has been found. A significant 67% and 77% reduction in the number of failure rates has been found for the 138 and 440 kV grids, respectively, for the period studied, in good correspondence with the decay in the sunspot numbers. No obvious correlation was found between power failures and geomagnetic activity, represented by (Kp) the planetary index or major geomagnetic storms (Dst) in the period, either on short or on long time scales. One suggested explanation associates the decrease in solar activity to the increased conductivity in the atmosphere caused by increase cosmic ray flux. Consequently there may be a reduction in the threshold voltage necessary to produce discharge atmospheric to cause failures in high-voltage grids. The global electric circuit described by the ionosphere-ground coupling (the electrosphere), plays an important role in explaining the reduction the failures. With increase in conductivity atmospheric discharges are less potent, resulting in fewer failures with the decreasing solar cycle / Doutorado / Energia Eletrica / Doutor em Engenharia Elétrica
13

Impactos do desempenho das emendas dos cabos de linhas de transmissão na confiabilidade de redes elétricas / Transmission lines cable splices performance impacts on electrical network reliability

Barbosa, Carlos David Franco, 1956- 18 August 2018 (has links)
Orientadores: Alberto Luiz Francato, Carlos Alberto Mariotoni / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-18T13:32:01Z (GMT). No. of bitstreams: 1 Barbosa_CarlosDavidFranco_D.pdf: 7182306 bytes, checksum: 6a8fd84aba169e2fceffb93e27a4c5b5 (MD5) Previous issue date: 2011 / Resumo: Esta tese tem como objetivo estudar métodos de planejamento da expansão da transmissão de energia elétrica em mercados de eletricidade re-estruturados, tanto em um ambiente tradicional quanto com a adoção de inovações tecnológicas. No trabalho são estudados procedimentos de campo para as linhas de transmissão, considerando economia e confiabilidade, principalmente em emendas a compressão para cabos ACSR (Aluminum Core Steel Reinforced). O trabalho descreve os resultados de pesquisas efetuadas com fabricantes e concessionárias usuárias das emendas a compressão e ainda sugere alguns procedimentos e rotinas de inspeções para melhorar a confiabilidade do sistema. Os resultados dos testes com as emendas, realizados em laboratório, serviram para dar suporte para a analise de falhas, subsidiando a avaliação das causas de falhas mais frequentes no ambiente competitivo. Por fim foram apresentadas tecnologias emergentes com possibilidade de redução da taxa de falhas nos sistemas de transmissão de energia elétrica bem como as recomendações de boas praticas para o setor / Abstract: This thesis has as objective to study electricity transmission expansion planning In re-structured markets, both traditional as well as with technological innovations. In the work are studied transmission lines field procedures considering economy and reliability, mainly ACSR (Aluminum Core Steel Reinforced) compression splices. The work describes compression splices field surveys with suppliers and users concessionaries and also suggest some procedures and inspections routines to improve system reliability. The results of laboratory splice tests helped the failure analysis and frequently failure causes on competitive environment. Finally it is presented emerging technologies with failure reduction possibilities for the electricity transmission systems and good practices recommendations for sector / Doutorado / Recursos Hidricos, Energeticos e Ambientais / Doutor em Engenharia Civil
14

APPLIED DEEP REINFORCEMENT LEARNING IN SMART ENERGY SYSTEMS MANAGEMENT

Moein Sabounchi (17565402) 07 December 2023 (has links)
<p dir="ltr">The horizon for inclusion of data-driven algorithms in cyber-physical systems is rapidly expanding due to evermore availability of high-performance computing tools and the inception of novel mathematical models in the fields of deep learning and reinforcement learning. In this regard, energy systems are a suitable candidate for data-driven algorithms utilization due to rapid expansion of smart measuring tools and infrastructure. Accordingly, I decided to explore the capabilities of deep reinforcement learning in control, security, and restoration of smart energy systems to tackle well-known problems such as ensuring stability, adversarial attack avoidance, and the black start restoration. To achieve this goal, I employed various reinforcement learning techniques in different capacities to develop transfer learning modules based on a rule-based approach for online control of the power system, utilized reinforcement learning for procedural noise generation in adversarial attacks against contingency detection in a power system and exploited multiple reinforcement learning algorithms to fully restore an energy system in an optimal manner. Per the results of these endeavors, I managed to develop a rule-based transfer learning logic to control the power system under various disturbance types and intensities. Furthermore, I developed an optimal adversarial attack module using a reinforcement-learning-based procedural noise generation to avoid detection by conventional deep-learning-based detection. Finally for the system restoration, the proposed intelligent restoration module managed to provide sustainable results for the black start restoration in energy system.</p>
15

OPTIMIZATION-BASED OPERATION AND CONTROL APPROACHES FOR IMPROVING THE RESILIENCE OF ELECTRIC POWER SYSTEMS

Dakota James Hamilton (17048772) 27 September 2023 (has links)
<p dir="ltr">The safe and reliable delivery of electricity is critical for the functioning of our modern society. However, high-impact, low-probability (HILP) catastrophic events (such as extreme weather caused by climate change, or cyber-physical attacks) pose an ever-growing threat to the power grid. At the same time, modern advancements in computational capabilities, communication infrastructure, and measurement technologies provide opportunities for new operation and control strategies that enhance the resilience of electric power systems to such HILP events. In this work, optimization-based operation and control approaches are proposed to improve resilience in two power systems applications. First, a real-time linearized-trajectory model-predictive controller (LTMPC) is developed for ensuring voltage, frequency, and transient (rotor angle) stability in systems engineered to operate as microgrids. Such microgrids are capable of seamlessly transitioning from grid-connected operation to an islanded mode and thus, enhance system resilience. The proposed LTMPC enables rapid deployment of such systems by reducing engineering costs and development time while maintaining stable operation. On the other hand, some power systems, such as distribution feeders, are not designed to operate as standalone microgrids. For these cases, a method is proposed for forming ad-hoc microgrids from intact sections of the damaged feeder in the aftermath of a HILP event. A feeder operating center-on-a-laptop (FOCAL) is introduced that coordinates the control of possibly hundreds of inverter-interfaced distributed energy resources (e.g., rooftop solar, battery storage) to improve system resilience. Theoretical analysis as well as numerical case studies and simulations of the proposed strategies are presented for both applications.</p>
16

Enhanced Passive RF-DC Converter Circuit Efficiency for Low RF Energy Harvesting

Chaour, Issam, Fakhfakh, Ahmed, Kanoun, Olfa 02 May 2017 (has links) (PDF)
For radio frequency energy transmission, the conversion efficiency of the receiver is decisive not only for reducing sending power, but also for enabling energy transmission over long and variable distances. In this contribution, we present a passive RF-DC converter for energy harvesting at ultra-low input power at 868 MHz. The novel converter consists of a reactive matching circuit and a combined voltage multiplier and rectifier. The stored energy in the input inductor and capacitance, during the negative wave, is conveyed to the output capacitance during the positive one. Although Dickson and Villard topologies have principally comparable efficiency for multi-stage voltage multipliers, the Dickson topology reaches a better efficiency within the novel ultra-low input power converter concept. At the output stage, a low-pass filter is introduced to reduce ripple at high frequencies in order to realize a stable DC signal. The proposed rectifier enables harvesting energy at even a low input power from −40 dBm for a resistive load of 50 kΩ. It realizes a significant improvement in comparison with state of the art solutions
17

METODOLOGIA PARA GERENCIAMENTO DE RISCOS EM PROJETOS DE TRANSMISSÃO DE ENERGIA ELÉTRICA COM FOCO NO PRAZO DE CONCLUSÃO APLICANDO O GERENCIAMENTO DE PROJETOS PELA CORRENTE CRÍTICA E SIMULAÇÃO DE MONTE CARLO / METHODOLOGY FOR RISK MANAGEMENT OF ELECTRIC ENERGY TRANSMISSION PROJECTS WITH FOCUS ON THE TIME FOR COMPLETION ADOPTING THE CRITICAL CHAIN AND MONTE CARLO SIMULATION FOR PROJECT MANAGEMENT

Pimentel, Jacinto Maia 18 October 2016 (has links)
Submitted by admin tede (tede@pucgoias.edu.br) on 2017-06-01T13:24:39Z No. of bitstreams: 1 JACINTO MAIA PIMENTEL.pdf: 3146885 bytes, checksum: d73d15b75ba44e1ab5fa45ebd06988f1 (MD5) / Made available in DSpace on 2017-06-01T13:24:39Z (GMT). No. of bitstreams: 1 JACINTO MAIA PIMENTEL.pdf: 3146885 bytes, checksum: d73d15b75ba44e1ab5fa45ebd06988f1 (MD5) Previous issue date: 2016-10-18 / The construction of electricity generation projects are held in places where there are specific conditions for its implementation, and it appears that these are not always close to the consumer markets. The energy needs to be transported to the consumption centers located many kilometers away, and to this end are used to power transmission lines. These developments are characterized by many different situations that impact on their time of completion. In order to pursue project management options so that deadlines are met, this research applies a risk management methodology for projects by means of the quantitative risk assessment. It is addressed to the energy transmission area with a focus on the project deadline. The proposed model adopts the Critical Chain Project Management – CCPM, whereby the appropriate activities duration are those achievable in the shortest time as possible. The use of CCPM calls for the application of buffers along the project schedule to control the uncertainties. The proposed methodology applies the Monte Carlo Simulation – MCS to the schedule, associating the Minimum, Most likely and Maximum times to the activities. The identified risks are related to these activities. The outcome resulting from the proposed methodology is quantitative and provides useful information to containment and contingency actions. / A construção dos empreendimentos de geração de energia elétrica é realizada nos locais onde existem condições específicas para sua implantação, e, nem sempre estes são próximos aos centros consumidores. A energia gerada necessita ser transportada para os centros de consumo localizados a muitos quilômetros de distância, e, para tal são utilizadas as Linhas de Transmissão de Energia. Estes empreendimentos caracterizam-se por encontrar situações diversas e que impactam no seu prazo de conclusão. Com o objetivo de buscar opções de gerenciamento de projetos para que os prazos sejam alcançados, esta pesquisa aplica uma metodologia para gestão dos riscos em projetos, com a aplicação de análise quantitativa dos riscos. Será aplicada na área de transmissão de energia com foco no prazo de conclusão. O modelo proposto utiliza o método do Gerenciamento de Projeto pela Corrente Crítica – CCPM, por meio do qual as durações das atividades consideradas são aquelas exequíveis no menor prazo possível. O uso da CCPM prevê a introdução de buffers no cronograma do projeto para controlar as incertezas. A metodologia proposta aplica ao cronograma a Simulação de Monte Carlo- SMC, associando às suas atividades o prazo Mínimo, Mais Provável e Máximo. Os riscos identificados são associados às atividades. O resultado da aplicação da metodologia proposta é uma análise dos riscos do projeto indicando a probabilidade de consumo dos buffers, as atividades que mais impactam no seu consumo e os riscos associados a estas. O resultado desta análise é quantitativa e gera informações úteis para ações de contenção e contingência.
18

Enhanced Passive RF-DC Converter Circuit Efficiency for Low RF Energy Harvesting

Chaour, Issam, Fakhfakh, Ahmed, Kanoun, Olfa 02 May 2017 (has links)
For radio frequency energy transmission, the conversion efficiency of the receiver is decisive not only for reducing sending power, but also for enabling energy transmission over long and variable distances. In this contribution, we present a passive RF-DC converter for energy harvesting at ultra-low input power at 868 MHz. The novel converter consists of a reactive matching circuit and a combined voltage multiplier and rectifier. The stored energy in the input inductor and capacitance, during the negative wave, is conveyed to the output capacitance during the positive one. Although Dickson and Villard topologies have principally comparable efficiency for multi-stage voltage multipliers, the Dickson topology reaches a better efficiency within the novel ultra-low input power converter concept. At the output stage, a low-pass filter is introduced to reduce ripple at high frequencies in order to realize a stable DC signal. The proposed rectifier enables harvesting energy at even a low input power from −40 dBm for a resistive load of 50 kΩ. It realizes a significant improvement in comparison with state of the art solutions
19

Electric Vehicles and the Utility Distribution Grid: An Impact Study

Matthew Brian Campbell (18086248) 01 March 2024 (has links)
<p dir="ltr"><b><i>Background</i></b><b>:</b> The increase in EV deployment is presenting numerous energy challenges to the utility distribution infrastructure. The energy demands created by EV charging sessions and the growing call to develop a network of DCFC charging facilities increases operational risk to the utilities in the ability to provide safe and reliable electricity to all customers.</p><p dir="ltr"><b><i>Purpose:</i></b> The purpose of this study is to identify the extent of impact to the utility distribution grid from an increasing EV (electric vehicle) adoption.</p><p dir="ltr"><b><i>Setting</i></b><b>: </b>In total, there were 3,020 rows of distribution circuit feeder data collected from the PG&E DIDF and National Grid NY System Reporting Tool between 2022 – 2023. Additionally, 48 documents, engineering reports, rate filings, articles, research studies, and utility whitepapers were examined.</p><p dir="ltr"><b><i>Research Design:</i></b> Impact analysis using a mixed methodology.</p><p dir="ltr"><b><i>Data Collection and Analysis:</i></b> A single research question was used to formulate an impact analysis to the utility distribution infrastructure under a mixed methodology. A quantitative analysis to determine circuit burden based on historical feeder capacity data and conduct hypothetical impact testing based on a set of ten variables. A qualitative analysis was administered to support these results and further design recommendations for the utility system under a logic model.</p><p dir="ltr"><b><i>Findings:</i></b> The PG&E and Utility National Grid EV and Circuit Impact Analysis demonstrated high susceptibility to overburden under a moderate number of level 2 EV chargers and significantly more when the loading impact was the result of DCFC facilities. The additional exploratory research yielded a consistent theme of mitigation strategies applicable to all electric utilities.</p><p><br></p><p dir="ltr"><b><i>Conclusions</i></b><i>:</i> Portions of the electric distribution infrastructure, operated by hundreds of utilities across the United States must be analyzed, upgraded, and adequately managed under systematic programs which promote facility upgrades, energy management, technology integration, such as AMI. Further, the execution of regulatory strategies for smart policy development and investment into hosting capacity tools are critical to reducing EV impact to the utility.</p><p dir="ltr"><b><i>Keywords</i></b><i>: </i>EV, electric utility, EV grid impacts, EV grid analysis, EV managed charging, EV AMI infrastructure.</p>
20

DYNAMIC SIMULATION TOOL FOR DISTRIBUTION FEEDERS USING A SPARSE TABLEAU APPROACH

Aravindkumar Rajakumar (17929553) 22 May 2024 (has links)
<p dir="ltr">Distributed energy resources (DERs), such as rooftop solar generation and energy storage systems, are becoming more prevalent in distribution systems. DERs are connected to the distribution system via power electronic converters, introducing faster dynamics in the system. Understanding the system dynamics under a high penetration of inverter-based DERs is critical for power system researchers and practitioners, driving the development of modeling techniques and simulation software. Aiming to reduce computational complexity, existing tools and techniques often employ various approximations. Meanwhile, modern advancements in computational hardware capabilities provide opportunities to include the faster time-scale dynamics. To address this, the primary objective of this thesis is to develop an open-source Python simulation package, Dynamic Simulation using Sparse Tableau Approach in Python, DynaSTPy (pronounced “dynasty”), capable of capturing the dynamics of all components in a distribution feeder. The distribution feeder is modeled as a system of Differential-Algebraic Equations (DAEs). Further, each component in the feeder is modeled based on the Sparse Tableau Approach (STA), which involves the representation of component model equations using sparse matrices, facilitating a systematic procedure to model the components and construct the system DAEs. In sinusoidal steady state, the DAEs can be represented in phasor form, extending the approach to perform power flow analysis of distribution feeders.</p>

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