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Mandali, Anusree. "Voltage Regulation Control on a Power System with Static Var Compensator." Cleveland State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=csu1504863882578828.
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Silva, Aguinaldo Silveira e. "Placement and control of static compensators for power system stability." Thesis, University of Manchester, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.311620.
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Horenský, Martin. "Dynamická kompenzace." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2014. http://www.nusl.cz/ntk/nusl-220932.
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This master’s thesis is focusing on compensation of reactive power, especially on creating demonstrative model of static var compensation unit (SVC). Main topic of thesis is to apply this device for fast balancing dynamic conversions of recieved reactive power. In theoretical part is described suitable method for determination of instantaneous power. Next, there is basic description of all means used for compensation of reactive power and detailed description of the SVC compensator. Practical part includes design of compensation unit and control program in LabVIEW. The pq theory is implemented for detection instantaneous power. The results of validating functionality of compensator are presented in the last part of thesis.
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Ahmed, Sheikh. "PMU based PSS and SVC fuzzy controller design for angular stability analysis." Thesis, Kansas State University, 2015. http://hdl.handle.net/2097/20547.
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Master of ScienceDepartment of Electrical and Computer Engineering
Shelli Starrett
Variability in power systems is increasing due to pushing the system to limits for economic purposes, the inclusion of new energy sources like wind turbines and photovoltaic, and the introduction of new types of loads such as electric vehicle chargers. In this new environment, system monitoring and control must keep pace to insure system stability and reliability on a wide area scale. Phasor measurement unit technology implementation is growing and can be used to provide input signals to new types of control. Fuzzy logic based power system stabilizer (PSS) controllers have also been shown effective in various studies. This thesis considers several choices of input signals, composed assuming phasor measurement availability, for fuzzy logic-based controllers. The purpose of the controller is to damp power systems’ low frequency oscillations. Nonlinear transient simulation results for a 4-machine two-area system and 50 machine system are used to compare the effects of input choice and controller type on damping of system oscillations. Reactive power in the system affects voltage, which in turn affects system damping and dynamic stability. System stability and damping can be enhanced by deploying SVC controllers properly. Different types of power system variables play critical role to damp power swings using SVC controller. A fuzzy logic based static var compensator (SVC) was used near a generator to damp these electromechanical oscillations using different PMU-acquired inputs. The goal was again improve dynamic stability and damping performance of the system at local and global level. Nonlinear simulations were run to compare the damping performance of different inputs on the 50 machine system.
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Sundström, Göran. "Analys av reaktiv effektinmatning till överliggande nät samt optimal kondensatordrift." Thesis, Umeå universitet, Institutionen för tillämpad fysik och elektronik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-136669.
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Bakgrunden till detta projekt är att Vattenfall Eldistribution AB (nedan kallat Vattenfall) kommer att införa ett avgiftssystem för inmatning av reaktiv effekt till sitt elnät. Avgiften införs till följd av problem på elnätet som orsakas av reaktiv effekt. Umeå Energi Elnät AB (nedan kallat Umeå Energi) har historiskt matat in reaktiv effekt vilket motiverade detta arbete som utreder den reaktiva effekten på Umeå Energis elnät samt bidrar med information om två alternativa tillvägagångssätt att bemöta avgiften. Alternativ 0 är att kompensationsutrustning inte installeras, utan att ett abonnemang på inmatning av reaktiv effekt upprättas. Alternativ 1 är att kompensationsutrustning installeras. För att utreda den reaktiva effekten erhölls och behandlades data på reaktiv effekt i Umeå Energis nät. Historisk kondensatordrift togs fram för år 2016 ur händelsehistoriken hos Umeå Energis driftcentral. Kondensatordriften år 2015 kunde enbart erhållas från ett tidigare arbete på Umeå Energi eftersom ett begränsat antal händelser lagras i händelsehistoriken. Genom att subtrahera kondensatorernas produktion från den reaktiva effekten i Umeå Energis anslutningspunkter som uppmätts av Vattenfall erhölls data som mer representerade underliggande fenomen på nätet. Utan kondensatordrift beräknades inmatningen enligt Vattenfalls definition uppgå till cirka 34 MVAr utifrån data från 2015 och 2016. För åren 2018 till och med 2023 beräknades ändringar i reaktiv effekt till följd av förändringar på Umeå Energis nät. Vid beräkningarna försummades ledningarnas induktiva karaktär, vilket gav ett tomgångsscenario med maximal produktion av reaktiv effekt. År 2023 beräknades inmatningen ska ha ökat till 59 MVAr till följd av förändringar på Umeå Energis nät. Med antagandet att Umeå Energi inte kommer att drifta kondensatorbatterierna så att inmatningen höjs föreslogs för alternativ 0 val av abonnemang på inmatning av reaktiv effekt för åren 2018 till och med 2023 utifrån de 34 MVAr som nämnts ovan och inverkan från förändringarna på nätet. År 2019 föreslogs ett abonnemang på 41 MVAr, och 2023 föreslogs ett på 59 MVAr. Kostnaderna för dessa beräknades enligt Vattenfalls tariff till 820 000 kr respektive 1 187 000 kr. Kostnaden för eventuell överinmatning av reaktiv effekt beräknades med tariffen för överinmatning årligen uppgå till maximalt 76 000 kr med 95 % sannolikhet enligt den korrigerade standardavvikelsen hos inmatningen utan kondensatordrift åren 2015 och 2016. Optimal kondensatordrift beräknades för åren 2015 och 2016 genom att addera den produktion av reaktiv effekt från befintliga kondensatorbatterier som gav minst absolutvärde i reaktiv effekt. Beroende på hur ofta kondensatordriften justerades erhölls olika resultat. En undersökning av störningar till följd av kondensatorkopplingar rekommenderas för att få en förståelse för förutsättningarna för optimal kondensatordrift. Det bedömdes inte ekonomiskt motiverbart med mer avancerad kompensationsteknik såsom statiska VAr-kompensatorer då variabla reaktorer kan kompensera dygns- och säsongsvariationer i reaktiv effekt. Den reaktiva effektproduktionen i ledningar är störst på 145 kV-nivån och kommer öka i framtiden på denna nivå. Det är därför sannolikt här kompensationsutrustning såsom reaktorer först bör installeras. För att kunna ta så bra beslut som möjligt angående den reaktiva effekten rekommenderas att snarast möjligt ingå ett arbetssätt som om avgiftssystemet redan tagits i bruk och utöka ett representativt dataunderlag.The background of this project is that Vattenfall Eldistribution AB (hereinafter referred to as Vattenfall) will establish a system of fees for input of reactive power. This will be done due to problems in the grid caused by reactive power. Umeå Energi Elnät AB (hereinafter referred to as Umeå Energi) has historically input reactive power, motivating this work which investigates the reactive power in the grid of Umeå Energi and provides information on two alternative approaches to responding to the fee. Alternative 0 entails no installation of compensation technology, and that a subscription for reactive power input is established instead. Alternative 1 entails that compensation technology is installed. To investigate the reactive power, data on reactive power in the grid of Umeå Energi were obtained and processed. Historical operations of capacitor banks for the year 2016 were obtained from the history of events of the control center at Umeå Energi. The operations of the capacitor banks during 2015 could only be obtained from an earlier work at Umeå Energi since the number of events stored in the history is limited. By subtracting the capacitor banks’ production from the reactive power measured by Vattenfall in the connections of Umeå Energi, data more representative of underlying phenomena were obtained. Without capacitor production of reactive power, the input was calculated according to the definition of Vattenfall to about 34 MVAr, by using data from 2015 and 2016. For the years 2018 through 2023, changes in reactive power due to changes in the grid of Umeå Energi were calculated. These calculations did not consider inductances, and thus yielded zero-load scenarios with maximum reactive power production. By the year of 2023, the input was calculated to have increased to 59 MVAr due to changes in the grid of Umeå Energi. Assuming that Umeå Energi will not operate the capacitors so that the input is increased, for alternative 0 subscriptions for input of reactive power were suggested for the years 2018 through 2023 by considering the abovementioned 34 MVAr and the changes in the grid. Subscriptions of 41 MVAr and 59 MVAr were suggested for the years 2019 and 2023 respectively. The costs of these were calculated with the fee specified by Vattenfall to SEK 820,000 and SEK 1,187,000 respectively. Calculations with the applicable fee yielded that the yearly cost of possible over-input could amount to a maximum of SEK 76,000 with a 95 % probability, using the corrected standard deviation of the input without capacitor production of reactive power for the years 2015 and 2016. Optimal capacitor bank operations were calculated for the years 2015 and 2016 by adding the production of reactive power from existing capacitor banks which yielded the minimum absolute reactive power. Depending on how often the capacitors were operated different results were obtained. An investigation of power quality disturbances due to capacitor bank operations is recommended to achieve an understanding of the conditions for optimal capacitor bank operations. It was not deemed economically justifiable to install more advanced compensation technologies such as static VAr compensators since variable reactors are able to compensate daily and seasonal variations in reactive power. The production of reactive power in cables is the largest on the 145 kV level and will increase in the future on this level. It is therefore likely here compensation technologies such as reactors should be installed first. To be able to make as good decisions as possible concerning the reactive power, it is recommended to as soon as possible commence a working method as if the fee system had already come into effect; thus increasing the amount of representative data.
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Silva, Júnior Gilson Soares da. "ANÁLISE DA INFLUÊNCIA DE UM COMPENSADOR ESTÁTICO DE REATIVOS NA OPERAÇÃO DE SISTEMA ELÉTRICO INDUSTRIAL COM COGERAÇÃO." Universidade Federal do Maranhão, 2008. http://tedebc.ufma.br:8080/jspui/handle/tede/312.
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Previous issue date: 2008-02-15In this work is analyzed the influence of a static var compensator (SVC) on the electromechanical stability of the electrical energy system of the industrial consumer ALUMAR that has a cogeneration. The main considerations on cogeneration systems, the FACTS Controllers and the systems involved in the analysis are described. Moreover, it is discussed the modeling of electrical system of ALUMAR highlighting the modeling updated and validated by the National Electric System Operator (ONS) and the modeling of cogenerators.
Análise da influência de um compensador estático de reativos (SVC) na estabilidade eletromecânica do sistema de energia elétrica do consumidor industrial ALUMAR o qual possui cogeração. Descrevem-se as principais particularidades sobre os sistemas de cogeração, os controladores FACTS e sobre os sistemas envolvidos na análise. Discute-se, ainda, a modelagem do sistema elétrico da ALUMAR, destacandose a modelagem atualizada e validada pelo Operador Nacional do Sistema (ONS) e a modelagem dos cogeradores.
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Hadjikypris, Melios. "Supervisory control scheme for FACTS and HVDC based damping of inter-area power oscillations in hybrid AC-DC power systems." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/supervisory-control-scheme-for-facts-and-hvdc-based-damping-of-interarea-power-oscillations-in-hybrid-acdc-power-systems(cc03b44a-97f9-44ec-839f-5dcbcf2801f1).html.
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Modern interconnected power systems are becoming highly complex and sophisticated, while increasing energy penetrations through congested inter-tie lines causing the operating point approaching stability margins. This as a result, exposes the overall system to potential low frequency power oscillation phenomena following disturbances. This in turn can lead to cascading events and blackouts. Recent approaches to counteract this phenomenon are based on utilization of wide area monitoring systems (WAMS) and power electronics based devices, such as flexible AC transmission systems (FACTS) and HVDC links for advanced power oscillation damping provision. The rise of hybrid AC-DC power systems is therefore sought as a viable solution in overcoming this challenge and securing wide-area stability. If multiple FACTS devices and HVDC links are integrated in a scheme with no supervising control actions considered amongst them, the overall system response might not be optimal. Each device might attempt to individually damp power oscillations ignoring the control status of the rest. This introduces an increasing chance of destabilizing interactions taking place between them, leading to under-utilized performance, increased costs and system wide-area stability deterioration. This research investigates the development of a novel supervisory control scheme that optimally coordinates a parallel operation of multiple FACTS devices and an HVDC link distributed across a power system. The control system is based on Linear Quadratic Gaussian (LQG) modern optimal control theory. The proposed new control scheme provides coordinating control signals to WAMS based FACTS devices and HVDC link, to optimally and coherently counteract inter-area modes of low frequency power oscillations inherent in the system. The thesis makes a thorough review of the existing and well-established improved stability practises a power system benefits from through the implementation of a single FACTS device or HVDC link, and compares the case –and hence raises the issue–when all active components are integrated simultaneously and uncoordinatedly. System identification approaches are also in the core of this research, serving as means of reaching a linear state space model representative of the non-linear power system, which is a pre-requisite for LQG control design methodology.
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Brough, Roger D. "A high pulse naturally commutated static VAr compensator." Thesis, University of Canterbury. Electrical and Electronic Engineering, 1995. http://hdl.handle.net/10092/5848.
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A new static VAr compensator (SVC) topology suitable for high voltage ac systems is proposed. This high pulse naturally commutated SVC is based on the ability of the ac/dc naturally commutated converter to regulate the absorption of reactive power and a novel method of achieving high pulse operation (i.e. with the dc ripple reinjection scheme). Steady state and dynamic operating performance of the scheme are tested in a variety of ac system conditions with the help of two models techniques, a scaled down equivalent in hardware and a high voltage representation in a computer simulation package (EMTDC-PSCAD).
There is a linear relationship between firing angle and reactive current, and the 36-pulse harmonic characteristic of the compensator current is consistantly maintained over this operating range and in a variety of ac system conditions. Its dynamic performance is compared to that of the thyristor controlled reactor (TCR), when operating in the same power system environment, showing that the proposed scheme's voltage control ability is consistently faster than the TCR.
The main difference in the compensator performances, however, is the proposed scheme's inherent temporary overload capability. This difference shows that there is the opportunity for the proposed scheme to supersede the TCR technology and further work to clarify the compensator's viability is considered to be worth while.
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Taberer, Marcel Wayne. "Transient analysis of erroneous tripping at grassridge static VAr compensator." Thesis, Nelson Mandela Metropolitan University, 2013. http://hdl.handle.net/10948/d1020918.
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The research work conducted and presented forward in this document is the evaluation of real time values obtained using three recording devices at two independent locations and implementing them as recorder devices in Eskom’s power system. The research work conducted was presented at an IEEE International Conference (ICIT2013) and Appendix A shows the accepted paper presented. A derived model within a simulation software package known as DIgSILENT PowerFactory is created and Electromagnetic Transient (EMT) studies are performed and then compared to the real time values obtained using the OMICRON CMC 356’s. Transformers are normally energised via a circuit breaker which is controlled by an auxiliary closing contact. By applying system voltage at a random instant in time on the transformer windings may result in a large transient magnetizing inrush current which causes high orders of 2nd harmonic currents to flow under no load conditions. A philosophy known to mitigate these currents is to energise the transformer by controlling each individual phase 120 degrees apart with the first pole closing at the peak on the voltage waveform. Transients produced due to 500MVA transformers been introduced into the power system at a certain space in time can cause nuisance tripping’s at the particular location where the respective transformer is energised. OMICRON EnerLyzer is the software tool used for the Comtrade recordings at both locations. Four independent case studies are generated within EnerLyzer software and the relevant Comtrade files are extracted for the four independent case studies relative to Transformer1 and Transformer2 switching’s. TOP software, which is a mathematical tool used to analyse Comtrade files, is then used to analyse and investigate the four case studies. Results from DIgSILENT PowerFactory are then generated according to the derived model. The results extracted depict three scenarios, indicating a power system that is weak, strong and specifically a power system that correlates to the actual tripping of a Static VAr Compensator (SVC). The results are all formulated and then evaluated in order to produce a conclusion and bring forward recommendations to Eskom in order to effectively ensure the Dedisa/Grassridge power system is reliable once again.
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Suhwail, Kareem M. "Synchrophasors' Application in SVC for Industrial Networks." Cleveland State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=csu1355884379.
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Fernando, Warnakulasuriya A. M. "Power quality improvement in power systems using a static VAR compensator." Thesis, California State University, Long Beach, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10638886.
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The primary purpose of a power system is to transform energy from one of its naturally obtainable forms into electricity, and then supply it through grids to points of consumption. With the increasing demand for electricity, more reliable methods are required to keep the quality of power in the desired range. This paper focuses on the impacts that a static var compensator (SVC) has on power quality. A two-area power system was used to demonstrate the power quality enhancements of a SVC, and simulations were done on the Real Time Digital Simulator (RTDS) and Electrical Transients Analyzer Program (ETAP). Simulations were performed for both steady-state and transient conditions to exhibit the dynamic capabilities of a SVC. Also, two different types of SVC controls were used and their effectiveness was analyzed. Simulations showed that the steady-state voltage, namely at bus 8 where the SVC was installed, improved from 0.94pu to 1.0pu. In addition, the voltage recovery time of bus 8 was improved from over 40s to approximately 2s.
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Mohd, Siam Mohd Fadzil. "The control of a static var compensator and active power filter." Thesis, Heriot-Watt University, 1998. http://hdl.handle.net/10399/1210.
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Idris, Ibrahim Idris Haroun. "Lab-scale thyristor rectifier and static VAR compensator circuits custom/typical applications /." Click here to view, 2009. http://digitalcommons.calpoly.edu/eesp/16/.
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Thesis (B.S.)--California Polytechnic State University, 2009.Project advisor: Taufik. Title from PDF title page; viewed on Jan. 28, 2010. Includes bibliographical references. Also available on microfiche.
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Reformat, Marek. "Application of genetic algorithms in control design for advanced static VAR compensator at ac/dc interconnection." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq23653.pdf.
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Holdsworth, Lee. "An investigation into the inherent robustness and optimal harmonic performance of the advanced static var compensator (ASVC)." Thesis, Northumbria University, 2001. http://nrl.northumbria.ac.uk/2144/.
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For many years, it was generally understood that a.c. transmission systems could not be controlled fast enough to handle dynamic system conditions. The dynamic system problems were usually handled by over-design, which resulted in under utilisation of the system. Flexible AC Transmission System (FACTS) devices play an important role in improving the dynamic performance of a power system and hence achieve better utilisation of the available system. They are principally employed to 'rapidly' control one or more of the three main parameters directly affecting a.c. power transmission, namely the system impedance, magnitude and phase angle of the system voltage. The Voltage Source Inverter (VSI) is the basic building block of most FACTS devices. The multi-level VSI topologies are becoming the favourite power circuits for the 2nd generation of FACTS shunt compensators. The research reported in this thesis is to investigate the reliability of Voltage Source Inverter topologies that are used in high power applications, mainly the Advanced Static VAr Compensator (ASVC). The inherent redundancy of the diode-clamped multi-level VSI topology, with respect to short-circuit and open- circuit device faults, is investigated using a space-vector nodal representation. The harmonic performance of the ASVC under normal and during 'device fault' operating conditions is also investigated. A new multi-level inverter topology is proposed to improve the robustness of the conventional diode-clamped VSI topology. Harmonic spectrum 'recovery' techniques to be utilised in the event of device failure are also investigated and discussed. An adaptive PWM controller is proposed to maintain an acceptable low order harmonic performance for the ASVC under normal and abnormal operating conditions. The results obtained show that the proposed system can maintain uninterrupted operational performance throughout certain device failure conditions. An experimental 3-level discharge path protection switch clamped (DPPSC) VSI system has been designed, constructed and analysed. To demonstrate the 3-level adaptive SHEM strategy, the adaptive DPPS controller was implemented on a TMS320F240 DSP evaluation module (EVM). The results were in good agreement with those predicted in the analytical and simulation parts of the work. The research carried out in this work showed that under loaded operating conditions, the low frequency harmonic components targeted by SHEM techniques are not fully eliminated from the output voltage spectrum. This investigation revealed that this is due to the harmonic interaction between the a.c. and d.c. sides of the multi-level inverter. A new 'Dynamic Selective Harmonic Elimination Modulation (DSHEM)' scheme is proposed to overcome this problem. The DSHEM dynamically adjusts the switching angles according to the system operating point. The proposed method is verified using simulation and the experimental model.
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Subsingha, Wanchai. "Analysis and control of the advanced static var compensator for normal and abnormal operating conditions in power systems." Thesis, Northumbria University, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.416348.
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Habtay, Yehdego Tekeste. "Advanced static VAr compensator for direct on line starting of induction motors in an interconnected offshore power system." Thesis, Heriot-Watt University, 2002. http://hdl.handle.net/10399/371.
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Almeida, Felipe Augusto Ferreira de [UNESP]. "Compensadores estáticos de reativos empregados em redes de baixa tensão com geradores distribuídos de energia." Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/146733.
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Instituto Federal de Educação, Ciência e Tecnologia de São Paulo (IFSP)
Este trabalho aborda o emprego do Compensador Estático de Reativos (SVC) em redes de baixa tensão com geração distribuída de energia, tendo como objetivo a compensação de tensão e de fator de potência. Os principais distúrbios de qualidade de energia elétrica em baixa tensão, bem como as normas e os limites operacionais para os principais indicadores foram revisados, visando confrontação com as situações resultantes da integração do SVC no sistema elétrico. O SVC possui operação estabelecida como carga reativa controlável em sistemas de transmissão de energia, fazendo parte dos condicionadores da tecnologia FACTS (Flexible AC Transmission Systems). A exploração desta tecnologia em outro nível de tensão é o objetivo deste trabalho. As análises foram realizadas através de simulações computacionais, desenvolvidas no ambiente MATLAB, contemplando o desenvolvimento de modelos relacionados com aplicações de RCT (Reator Controlado a Tiristor), FC (Capacitor Fixo), do CCT (Capacitor Chaveado a Tiristor) e de um sistema de geração distribuída de energia elétrica trifásico em uma rede de baixa tensão a quatro fios. A metodologia para o dimensionamento dos elementos passivos dos condicionadores é apresentada, bem como a análise dos valores de potência reativa, fator de potência, distorções harmônicas e a avaliação da necessidade de utilização ou não de filtros passivos. A teoria da potência conservativa (TPC) é a metodologia utilizada para definição das grandezas elétricas e fatores de conformidade. Por fim, as características operacionais de um SVC aplicado a uma rede de baixa tensão a quatro fios são exploradas através dos resultados de simulação, com o objetivo de demonstrar a manutenção de suas características operacionais estabelecidas, no nível de baixa tensão, e apontar aspectos diferenciados quanto à regulação de fator de potência e da forma de tensão providos pelo SVC, para servir como informação de confronto frente a outras tecnologias comumente utilizadas neste nível de tensão.
This paper discusses the use of Static Var Compensator (SVC) on low voltage grids with distributed generation with the aim of voltage and power factor compensation. The main electrical power quality disturbances at low voltage as well as the rules and operational limits for the main indicators were reviewed aiming to confront the situations resulting from SVC integration in the electrical system. SVC has established operation as controllable reactive load in power transmission systems, being part of FACTS (Flexible AC Transmission Systems) technology conditioners. The application of this technology in another level of tension is the objective of this work. The analyzes were carried out through computer simulations developed in the MATLAB environment, including the development of models related to RCT (Thyristor Controlled Reactor), FC (Fixed Capacitor), CCT (Thyristor Switching Capacitor) and a threephase electric power distributed generation system in a four-wire low voltage grid. The methodology for the dimensioning of the passive elements of the conditioners is presented, as well as the analysis of the values of reactive power, power factor, harmonic distortions and the evaluation of the need to use passive filters. The conservative power theory (CPT) is the methodology used to define the electrical magnitudes and compliance factors. Finally, the operational characteristics of a SVC applied to a low-voltage four-wire network are exploited through the simulation results, in order to demonstrate the maintenance of its established operational characteristics at the low voltage level and to point out different aspects as well as the power factor regulation and voltage form provided by the SVC, to serve as confronting information.
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Bento, José Antônio Chiabai. "Requisitos de suporte de potência reativa para operação de usinas eólicas." Universidade Federal de Juiz de Fora, 2013. https://repositorio.ufjf.br/jspui/handle/ufjf/1163.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
A penetração de parques eólicos nos sistemas elétricos de potência tem apresentado um grande crescimento no Brasil e no mundo devido à disponibilidade da matéria prima, os ventos, e à necessidade de reformulação das matrizes energéticas a fim de reduzir os impactos ambientais decorrentes da geração de energia elétrica. Porém, as usinas eólicas apresentam variações nos despachos de potência devido à variabilidade de velocidade dos ventos. Estas variações causam impactos no sistema, podendo afetar a confiabilidade e a estabilidade de tensão. Além disto, a operação de determinados tipos de aerogeradores requer suporte adicional de potência reativa. Uma opção para aumentar as margens operativas e acomodar as intermitências de regime dos ventos em sistemas elétricos de potência consiste na utilização de compensadores estáticos de reativos (CER) junto às usinas eólicas. Estes equipamentos FACTS (Flexible AC Transmission Systems) provêm suporte de potência reativa variável e de rápido controle, de acordo com os requisitos operacionais dos aerogeradores. Neste sentido, o presente trabalho apresenta uma metodologia para ajuste ótimo dos parâmetros do CER visando dar suporte de potência reativa para a operação de usinas eólicas em sistemas elétricos de potência. Para representar as intermitências no despacho de potência dos aerogeradores, a metodologia proposta considera diferentes cenários de vento. O problema é modelado através de fluxo de potência ótimo (FPO), associado à técnica de decomposição matemática de Benders. Os parâmetros de ajuste do CER são a tensão de referência e o coeficiente de inclinação da curva característica deste equipamento em regime permanente. Destaca-se que o ajuste ótimo deste coeficiente é inédito na literatura especializada. Testes com sistemas do IEEE são realizados para validar a metodologia proposta.
The penetration of wind farms in power systems has shown tremendous growth in Brazil and in the world due to the availability of the raw material, the wind, and the need to redefine the energy mix to reduce the environmental impacts from the electrical energy generation. However, the wind farms have variable outputs due to the variation of wind speeds. These outputs impact the power system and can affect the reliability and the voltage stability. Besides, the operation of some aerogenerators requires additional support of reactive power. An option for handling this feature and increasing the operative margins of power systems is the use of static VAr compensators (SVC) together with the wind farms. These FACTS devices (Flexible AC Transmission Systems) provide a variable reactive power support, with a fast control according to the operational requirements of the aerogenerators. In this sense, this work presents a methodology for the optimal adjustment of the SVC parameters to give reactive power support for wind farms operating in power systems. The proposed methodology considers different wind scenarios to represent the variations of the wind farms outputs. The problem is modeled through an optimal power flow (OPF) and the Benders decomposition technique. The SVC parameters for adjustment are its reference voltage and the coefficient of its characteristic curve in stable state. It can be highlighted that the adjustment of this coefficient is innovative for the literature. Tests with systems of the IEEE are performed to validate the proposed methodology.
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Banejad, Mahdi. "Identification of damping contribution from power system controllers." Thesis, Queensland University of Technology, 2004. https://eprints.qut.edu.au/15851/1/Mahdi_Banejad_Thesis.pdf.
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With the growth of power system interconnections, the economic drivers encourage the electric companies to load the transmission lines near their limits, therefore it is critical to know those limits well. One important limiting issue is the damping of inter-area oscillation (IAO) between groups of synchronous machines. In this Ph.D. thesis, the contribution of power system components such as load and static var compensators (SVC) that affect the IAO of the power system, are analysed. The original contributions of this thesis are as follows: 1-Identification of eigenvalues and mode shapes of the IAO: In the first contribution of this thesis, the eigenvalues of the IAO are identified using a correlation based method. Then, the mode shape at each identified resonant frequency is determined to show how the synchronous generators swing against each other at the specific resonant frequencies. 2-Load modelling and load contribution to damping: The first part of this contribution lies in identification of the load model using cross-correlation and autocorrelation functions . The second aspect is the quantification of the load contribution to damping and sensitivity of system eigenvalues with respect to the load. 3- SVC contribution to damping: In this contribution the criteria for SVC controller redesign based on complete testing is developed. Then the effect of the SVC reactive power on the measured power is investigated. All of the contributions of this thesis are validated by simulation on test systems. In addition, there are some specific application of the developed methods to real data to find a.) the mode shape of the Australian electricity network, b.) the contribution of the Brisbane feeder load to damping and c.) the effect of the SVC reactive power of the Blackwall substations on the active power supplying Brisbane.
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Banejad, Mahdi. "Identification of Damping Contribution from Power System Controllers." Queensland University of Technology, 2004. http://eprints.qut.edu.au/15851/.
Full textAbstract:
With the growth of power system interconnections, the economic drivers encourage the electric companies to load the transmission lines near their limits, therefore it is critical to know those limits well. One important limiting issue is the damping of inter-area oscillation (IAO) between groups of synchronous machines. In this Ph.D. thesis, the contribution of power system components such as load and static var compensators (SVC) that affect the IAO of the power system, are analysed. The original contributions of this thesis are as follows: 1-Identification of eigenvalues and mode shapes of the IAO: In the first contribution of this thesis, the eigenvalues of the IAO are identified using a correlation based method. Then, the mode shape at each identified resonant frequency is determined to show how the synchronous generators swing against each other at the specific resonant frequencies. 2-Load modelling and load contribution to damping: The first part of this contribution lies in identification of the load model using cross-correlation and autocorrelation functions . The second aspect is the quantification of the load contribution to damping and sensitivity of system eigenvalues with respect to the load. 3- SVC contribution to damping: In this contribution the criteria for SVC controller redesign based on complete testing is developed. Then the effect of the SVC reactive power on the measured power is investigated. All of the contributions of this thesis are validated by simulation on test systems. In addition, there are some specific application of the developed methods to real data to find a.) the mode shape of the Australian electricity network, b.) the contribution of the Brisbane feeder load to damping and c.) the effect of the SVC reactive power of the Blackwall substations on the active power supplying Brisbane.
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Goldoost, Soloot Reza. "Wide-area damping control through inverse filtering technique." Thesis, Queensland University of Technology, 2016. https://eprints.qut.edu.au/95937/4/Reza%20Goldoost%20Soloot_Thesis.pdf.
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This thesis proposes a new wide-area controller for enhancing the stability of power systems by damping inter-area oscillations. The obtained controller is a new nonlinear controller that accomplishes the task by using data from PMUs employed throughout the network. The controller improves the damping of inter-area oscillations by providing a supplementary control input for several controllable devices such as excitation systems of synchronous generators and Static Var Compensators. The novel nonlinear inverse filtering controller is developed and investigated in different network configurations in the thesis.
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Loureiro, Pedro da Cruz. "Controle de tensão e harmônicos por compensador estático de reativos com ajuste de parâmetros via redes neurais artificiais." Universidade Federal de Juiz de Fora, 2012. https://repositorio.ufjf.br/jspui/handle/ufjf/1785.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Neste trabalho é proposta a aplicação de redes neurais artificiais para ajuste de parâmetros de um compensador estático de reativos, para controle de tensão e harmônicos. Devido à intensa produção de correntes harmônicas e possíveis afundamentos de tensão em instalações industriais como o forno a arco, é necessário um sistema de controle eficiente e robusto. Além disso, os sistemas elétricos de potência se encontram em um cenário com a presença cada vez maior de geração distribuída, cargas não-lineares e forte tendência à operação no contexto das smartgrids e microgrids. Sendo assim, o suporte de reativos deve ser adequado a esses sistemas, podendo atuar de forma rápida, precisa e confiável. Uma possível solução é a utilização de um compensador estático de reativos (CER) com função adicional de filtragem no ponto onde se deseja controlar a tensão e a distorção harmônica. Entretanto, para o correto funcionamento, é necessário um sistema preciso para o ajuste dos parâmetros do CER, ou seja, determinar os ângulos de disparo dos tiristores e o número de bancos de capacitores a serem ligados. Neste trabalho é proposta uma estratégia de controle via redes neurais artificiais, treinadas para o reconhecimento de padrões de operação em regime permanente e definição da configuração do CER, conferindo inteligência ao equipamento. Os desenvolvimentos propostos foram implementados no ambiente MatLab®. A validação do método é feita através de simulações em sistemas-teste, presentes na literatura técnica, utilizando o fluxo de potência pelo método de injeção de correntes trifásico harmônico. Os resultados obtidos mostram as vantagens da utilização da estratégia proposta.
In this work, an artificial neural network-based static var compensator tuning is proposed for voltage and harmonic distortion control. Due to intense harmonic current injection and possible voltage sags produced by industrial facilities such as arc furnaces, an efficient robust control system is needed. Besides, electrical power systems face a new scenario with high penetration of distributed generation and non-linear loads and increased smart grid and microgrid trends. Therefore, the available reactive power sources must be able to provide system control in order to operate the system in a fast, accurate and reliable way. The application of a static var compensator (SVC) with additional filtering function at the controlled node is a possible solution. However, a precise SVC parameters tuning is needed, in order to make the system to work properly. In this work, a control strategy based on artificial neural networks is proposed. The neural networks are trained to recognize steadystate operating patterns and give the SVC adjustment. The proposed technique was implemented in the MatLab® environment. The methodology is validated by simulations in test-systems available in technical literature, using the three-phase harmonic current injection method power flow. Results show the advantages of the proposed methodology.
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QIU, JIN-LONG, and 邱金龍. "Microprocessor based static var compensator design." Thesis, 1991. http://ndltd.ncl.edu.tw/handle/05705839542679534547.
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WAN, Hsing-ho, and 萬興和. "A New Advanced Static VAR Compensator." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/45515504229565768099.
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GONG, RONG-YUAN, and 龔榮源. "A sinusoidal pulsewidth modulated static VAR compensator." Thesis, 1987. http://ndltd.ncl.edu.tw/handle/60829762517807389163.
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Lin, Zun-Liang, and 林俊良. "A study of static var compensator on power factor correction." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/48961404511017004816.
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Hsieh, Lu-Ti, and 謝律迪. "Study and Implementation of Induction Generator with Static VAR Compensator." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/09892382011246382495.
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碩士國立臺北科技大學
電機工程系碩士班
92
This thesis has two research objectives. The first objective is for a conversion power supply system of self-excited induction generator. The second is for an induction generation system with current-type static VAR compensator (SVC). An induction generator has many favorable advantages including lower setup and maintenance cost, simple construction, inherent over load and short circuit protection, and high power-weight ratio. However, there are drawbacks of the conventional induction generator. For small capacity systems, the output voltage and frequency are easily and instantaneously affected by rotational speed of rotor, system load, and the power factor. It leads that the output frequency at the generator terminal is irritable and the voltage regulation is deteriorated. In the proposed generation system, the output voltage of the generator is converted by a three-phase converter and filtered by an LC filter. The obtained voltage is then treated as the input DC source of an inverter. As a result, the output supply frequency is independent of generator’s rotor rotational speed and can be dynamically regulated to the set-point frequency by adjust the inverter. In addition, an induction generation system with current-type static VAR compensator (SVC) is proposed. SVC is connected in parallel with excitation capacitors and used to control the reactive power at the generator terminals. Based on the load requirements and system parameters, SVC generates reactive power to the generation system and suppresses voltage variation caused by load and rotor rotational speed changes. Simulation and experiment results show that the conversion power supply system of self-excited induction generator can dynamically regulate the frequency of output voltage to the desired set point. Moreover, the induction generator system with current-type static VAR compensator can improve the stability of output voltage. Consequently, the proposed induction generator system has fast and superior dynamic response with respect to the variations of voltage and rotational speed. Also, the supply quality and stability of the output voltage are improved.
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Chen, Chun-Kai, and 陳淳楷. "Static Var Compensator for Improving Shipboard Electric Power System Stability." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/16029838310927628562.
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碩士國立海洋大學
電機工程學系
91
The shipboard electric power system is an independent system of which the required reliability is higher than that of the seashore power system. Because of the frequent load variation, the generating unit shall have fast and stable responding capability. Proper application of compensating devices will improve the damping of electromechanical oscillations and thus the stability of the system. This thesis studies a practical shipboard electric power system, with emphasis placed on investigating the effect of the static var compensator (SVC) on the system dynamic behaviors by using the method of eigenanalysis. Time-domain simulations of the system under different disturbances are performed for verification.
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Shih-Wei, Sun, and 孫士偉. "Ehancement of Transmission System Stability by Applying Static Var Compensator." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/36911736827233227208.
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碩士南台科技大學
電機工程系
98
ABSTRACT The main purpose of this thesis is to investigate the power system voltage stability and transient stability analysis. In the thesis, the Taiwan power system is selected for study. Based on the peak operation condition of Taiwan power system, the P-V and Q-V curves can be obtained by executing the voltage stability analysis in various N-1 and N-2 transmission line tripping contingencies. The P-V curve can denote the voltage collapse point and transfer power limit while the Q-V curve can identify the reactive power margin of the transmission lines. By the way, transient stability analysis is also performed to verify the system can be recovered to stable or not by examining the bus voltage and transmission line power flow after the contingency. In addition, the static var compensator are considered to be installed at the critical buses with different capacities to enhance the system stability and to avoid system from collapse.
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Agrawal, Shweta, and Suchitra Singh. "Study of subsynchronous resonance and its countermeasure using static VAR compensator." Thesis, 2010. http://ethesis.nitrkl.ac.in/1786/1/Thesis-Shweta.pdf.
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This project includes the study of Subsynchronous resonance (SSR) phenomenon which occurs in a power system having series capacitor compensated transmission line. Static VAR compensators can be used to damp SSR oscillations besides controlling the system voltage. The First IEEE benchmark model and eigenvalue techniques are applied in the project to study the behavior of turbo-generator connected to the series compensated transmission line.
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Gao, Yang. "A single phase static var compensator using a voltage source GTO inverter." 1993. http://hdl.handle.net/1993/29384.
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陳快前. "The application of static var compensator for load compensation and balance control." Thesis, 1990. http://ndltd.ncl.edu.tw/handle/16094355654810410078.
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Santosh, Kumar A. "Voltage Stability Analysis of Unbalanced Power Systems." Thesis, 2016. http://etd.iisc.ac.in/handle/2005/3065.
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The modern day power system is witnessing a tremendous change. There has been a rapid rise in the distributed generation, along with this the deregulation has resulted in a more complex system. The power demand is on a rise, the generation and trans-mission infrastructure hasn't yet adapted to this growing demand. The economic and operational constraints have forced the system to be operated close to its design limits, making the system vulnerable to disturbances and possible grid failure. This makes the study of voltage stability of the system important more than ever.
Generally, voltage stability studies are carried on a single phase equivalent system assuming that the system is perfectly balanced. However, the three phase power system is not always in balanced state. There are a number of untransposed lines, single phase and double phase lines. This thesis deals with three phase voltage stability analysis, in particular the voltage stability index known as L-Index. The equivalent single phase analysis for voltage stability fails to work in case of any unbalance in the system or in presence of asymmetrical contingency. Moreover, as the system operators are giving importance to synchrophasor measurements, PMUs are being installed throughout the system. Hence, the three phase voltages can be obtained, making three phase analysis easier.
To study the effect of unbalanced system on voltage stability a three phase L-Index based on traditional L-Index has been proposed. The proposed index takes into consideration the unbalance resulting due to untransposed transmission lines and unbalanced
loads in the system. This index can handle any unbalance in the system and is much more realistic. To obtain bus voltages during unbalanced operation of the system a three phase decoupled Newton Raphson load ow was used.
Reactive power distribution in a system can be altered using generators voltage set-ting, transformers OLTC settings and SVC settings. All these settings are usually in balanced mode i.e. all the phases have the same setting. Based on this reactive power optimization using LP technique on an equivalent single phase system is proposed. This method takes into account generator voltage settings, OLTC settings of transformers and SVC settings. The optimal settings so obtained are applied to corresponding three phase system. The effectiveness of the optimal settings during unbalanced scenario is studied. This method ensures better voltage pro les and decrease in power loss.
Case studies of the proposed methods are carried on 12 bus and 24 bus EHV systems of southern Indian grid and a modified IEEE 30 bus system. Both balanced and unbalanced systems are studied and the results are compared.
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Santosh, Kumar A. "Voltage Stability Analysis of Unbalanced Power Systems." Thesis, 2016. http://hdl.handle.net/2005/3065.
Full textAbstract:
The modern day power system is witnessing a tremendous change. There has been a rapid rise in the distributed generation, along with this the deregulation has resulted in a more complex system. The power demand is on a rise, the generation and trans-mission infrastructure hasn't yet adapted to this growing demand. The economic and operational constraints have forced the system to be operated close to its design limits, making the system vulnerable to disturbances and possible grid failure. This makes the study of voltage stability of the system important more than ever.
Generally, voltage stability studies are carried on a single phase equivalent system assuming that the system is perfectly balanced. However, the three phase power system is not always in balanced state. There are a number of untransposed lines, single phase and double phase lines. This thesis deals with three phase voltage stability analysis, in particular the voltage stability index known as L-Index. The equivalent single phase analysis for voltage stability fails to work in case of any unbalance in the system or in presence of asymmetrical contingency. Moreover, as the system operators are giving importance to synchrophasor measurements, PMUs are being installed throughout the system. Hence, the three phase voltages can be obtained, making three phase analysis easier.
To study the effect of unbalanced system on voltage stability a three phase L-Index based on traditional L-Index has been proposed. The proposed index takes into consideration the unbalance resulting due to untransposed transmission lines and unbalanced
loads in the system. This index can handle any unbalance in the system and is much more realistic. To obtain bus voltages during unbalanced operation of the system a three phase decoupled Newton Raphson load ow was used.
Reactive power distribution in a system can be altered using generators voltage set-ting, transformers OLTC settings and SVC settings. All these settings are usually in balanced mode i.e. all the phases have the same setting. Based on this reactive power optimization using LP technique on an equivalent single phase system is proposed. This method takes into account generator voltage settings, OLTC settings of transformers and SVC settings. The optimal settings so obtained are applied to corresponding three phase system. The effectiveness of the optimal settings during unbalanced scenario is studied. This method ensures better voltage pro les and decrease in power loss.
Case studies of the proposed methods are carried on 12 bus and 24 bus EHV systems of southern Indian grid and a modified IEEE 30 bus system. Both balanced and unbalanced systems are studied and the results are compared.
36
陳俊昌. "Static Var Compensator and Battery Energy Storage System for Shipboard Electirc Power System Stability." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/80152075190708545361.
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碩士國立海洋大學
電機工程學系
90
The shipboard electric power system is an independent system of which the required reliability is higher than that of the seashore power system. Because of the frequent load variation, the generating unit shall have fast and stable response. Equipped with properly tuned additional Static Var Compensator will improve the damping of electromechanical oscillations in power system. Battery Energy storage system can provide simultaneously control of both its active and reactive power to improve power system operation and control. The main purpose of this thesis is to study the stability of the shipboard electric power system on analyzing the effect of the Static Var Compensator and Battery Energy Storage System on overall system dynamic behaviors. A sample shipboard electric power system is taken as the study system. Based on the results analyzed and verified from the time-domain simulations, this paper shows that Battery Energy Storage System and Static Var Compensator can offer an important resource for improving shipboard electric power system operation.
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Tung, Shuo-Hsuan, and 董碩軒. "Effects of Three-phase Voltage Unbalance on Harmonic Currents of a Static Var Compensator." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/hu86dh.
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碩士國立雲林科技大學
電機工程系
104
This thesis analyzes harmonic currents produced by a three-phase delta-connected static var compensator (SVC) under voltage unbalance. Three-phase voltage unbalance is a commonly encountered disturbance but voltage unbalance factor (UBF) is in general lower than 5%. In this thesis, the effects of voltage unbalance on harmonic currents of a three-phase thyristor-controlled reactor (TCR) are made salient by considering a high value of voltage UBF of 25%. The analytical model of TCR current waveform is analyzed by Fourier analysis. The total harmonic distortion and UBF of harmonic currents can then be obtained. To validate the harmonic analysis, time domain dynamic simulation using the ATP (Alternative Transients Program) has been carried out. Simulation results show that harmonic currents of the TCR under voltage unbalance can be accurately predicted by the proposed analytical model.
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Lin, Kun-Yeh, and 林昆燁. "Coordination Control of Static Var Compensator and Onload Tap Changer Transformerby Using Fuzzy Logic." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/88834152008028644983.
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碩士國立中正大學
電機工程研究所
99
In this study, the goal is to investigate the power quality problems that occur in a Taipower’s primary substation system (P/S), where the P/S feeds electric power to several steel-making customers. Recently, due to the operations of these EAF loads, it is observed that serious voltage fluctuations occurred at the bus that connected to the P/S transformers. The on-load tap changers (OLTCs) of the transformers have thus frequently switched on and off, which deteriorate the transformer life and also affect the supply power quality. This study analyzes the power quality impact of severely load variations on the feeder under the area where has several steel industry customers. It uses simulation techniques and accurate equipment models to test the simulation, and assess the effects of installing SVC to support the installation of SVC in the existing area. In order to improve the switching situation of OLTC, this study adopts the fuzzy control for OLTC and SVC coordination. And it explores the relation between the OLTC operation and the voltage flicker to clarify the result of OLTC malfunction. Finally, it assesses the power quality of a primary substation with large arc furnace loads.
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Huang, Jian-Long, and 黃健龍. "Design of a Grey Decision Prediction Controller for Induction Generator System with Static VAR Compensator." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/ysv63d.
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碩士國立臺北科技大學
電機工程系所
93
This thesis integrates the inverting power supply system and the Static VAR Compensator (SVC) to form an inverting power supply system for induction generator with SVC. The advantages of induction generator includes lower cost, simple structure, high power-weight ratio, protection ability of over load and short circuit, so that the induction generators are widely used in smaller capacity power station. However, there are drawbacks of the conventional induction generators, the output voltage and frequency are easily and instantaneously affected by rotational speed of rotor, system load, and the power factor. It leads that the output frequency at the generator terminal is irritable and the voltage regulation is deteriorated. To solve the problems, this thesis proposes a novel induction generator system, which combines the inverting power supply system and SVC, to restrain voltage fluctuation due to the change load of induction generator system. As a result, the output voltage will steadily remain at the set point and increase the quality of output voltage of induction generator. For the inverting power supply system, the output voltage of the generator is converted by a three-phase converter, filtered by an L-C filter, and then supplied to inverter as the DC input. As a result, the output frequency is independent of generator’s rotor speed, and the output frequency can be dynamically regulated to the set-point frequency by adjust the inverter. In addition, SVC can effectively improve the voltage regulation performance of induction generator system in the conditions of high voltage, loading, and unloading. Furthermore, Grey Decision Prediction Controller (GDPC) is embedded into the two modules of induction generator system. The grey prediction function can predict the trend of the system response and proactively compensate the considered system. In addition, the grey decision function can dynamically regulate steps of grey prediction to enhance the performance of dynamic behaviors of the inverting power supply system and SVC. Experiment results show that the proposed induction generator system has quick and excellent dynamic response in the variations of voltage and rotor’s speed. The designed system can dramatically improve the supply quality of elf-excited induction-generator and the stability of output voltage.
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Chen, Meng Bo, and 陳孟柏. "Capacity Estimation and Harmonic Resonance Improvement of Static Var Compensator for Steel-Making Factory with Electric Arc Furnace." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/77523m.
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liao, ching-yu, and 廖慶雨. "A Study on the Application of a Single Static VAR Compensator for Flicker Reduction in Multi-Voltage Arc Furnaces." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/72301054564544579621.
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碩士逢甲大學
電機工程所
92
An ARC furnace load may cause voltage flicker and low power factor, which adversely affects power quality on the distribution power system. One way to alleviate the problem is to install a static var compensator in shunt with the distribution line. Traditionally, it requires different voltage-level static var compensators in multi-voltage arc furnaces. This approach is effective for flicker reduction, but needs higher investment. In order to use a single static var compensator in multi-voltage arc furnaces for flicker reduction, a programmable logical controller is designed in this thesis, The controller detects the operation conditions of the furnaces and provides the information for firing angle setting of the compensator. The effect on flicker reduction of the scheme is not as good as the tradition one, but meets the regulation of Taiwan Power Company.
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Mazur, Ronald Wayne. "Damping of power system harmonic resonances using firing angle modulation of the thyristor controlled reactor of a static var compensator." 1989. http://hdl.handle.net/1993/16969.
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