Solar PV-based distributed generation has increased significantly over the last few years, and the rapid growth is expected to continue in the foreseeable future. As the penetration levels of distributed generation increase, power systems will become increasingly decentralized with bi-directional flow of electricity between the transmission and distribution networks. To manage such decentralized power systems, planners and operators need models that accurately reflect the structure of, and interactions between the transmission and distribution networks. Moreover, algorithms that can simulate the steady state and dynamics of power systems using these models are also needed. In this context, integrated transmission and distribution system modeling and simulation has become an important research area in recent years, and the primary focus so far has been on studying the steady state response of power systems using integrated transmission and distribution system models. The primary objective of this dissertation is to develop an analysis approach and a program that can simulate the dynamics of three phase, integrated transmission and distribution system models, and use the program to demonstrate the advantages of evaluating the impact of solar PV-based distributed generation on power systems dynamics using such models. To realize this objective, a new dynamic simulation analysis approach is presented, the implementation of the approach in a program is discussed, and verification studies are presented to demonstrate the accuracy of the program. A new dynamic model for small solar PV-based distributed generation is also investigated. This model can interface with unbalanced networks and change its real power output according to the incident solar irradiation. Finally, application of the dynamic simulation program for evaluating the impact of solar PV units using an integrated transmission and distribution system model is discussed. The dissertation presents a new approach for studying the impact of solar PV-based distributed generation on power systems dynamics, and demonstrates that the solar PV impact studies performed using the program and integrated transmission and distribution system models provide insights about the dynamic response of power systems that cannot be obtained using traditional dynamic simulation approaches that rely on transmission only models. / Ph. D. / To ensure that electricity is delivered to consumers in a reliable manner, power system planners and operators rely on computer-based modeling and analysis of the electric grid. The software currently being used for this purpose are designed to simulate either the high voltage transmission networks, or the low voltage distribution networks. Till now these software have worked well as the electricity flow in the electric grid is largely unidirectional, from the transmission network to the distribution network. Neglecting the distribution network topology in transmission network models or vice-versa in such a structure of the electric grid does not introduce significant calculation errors. However, the rapid growth of consumer-owned and operated solar photovoltaics (PV) based distributed generation over the last few years, which is expected to continue in the foreseeable future, has necessitated a rethink of this modeling and analysis paradigm. As the penetration levels of distributed generation increase, the electric grid will become increasingly decentralized and there will be bi-directional flow of electricity between the transmission and distribution networks. Accurate analysis of such a decentralized electric grid cannot be performed if either the distribution or the transmission network topology is neglected in the models. Integrated transmission and distribution system modeling and simulation, where transmission and distribution networks are modeled as one single unit, has, therefore, become an important research area in recent years. This dissertation makes a contribution to this research area by presenting an analysis approach and a program that can be used to simulate the dynamics (time varying behavior of the electric grid when subjected to disturbances such as short-circuits) of integrated transmission and distribution system models. A dynamic model of solar PV-based distributed generation that can be used to simulate their behavior during dynamic simulations is also investigated. Finally, an application of the program is discussed where the impact of solar PV-based distributed generation on the dynamics of the electric grid is studied by using the solar PV model and an integrated transmission and distribution system model. The dissertation shows that by simulating integrated transmission and distribution system models using the dynamic simulation program, insights about the impact of solar PV-based distributed generation on the dynamics of the electric grid can be obtained, which the transmission only models cannot provide.

Att ha ständig tillgång till ett hälsosamt, rent och gärna gott dricksvatten tas idag ofta som självklart av många människor i Sverige. Sveriges sammanlagda nybildning av vatten innebär idag inga problem för dricksvattenförsörjningen om man bortser från ojämn fördelning av vattentillgångar samt lokala kvalitetsproblem. Många områden förses med dricksvatten från något av landets omkring 2000 vattenverk. En del får sitt vatten från enskilda brunnar, medan vissa har löst vattenfrågan tillsammans med andra i samfälligheter. Vissa samfälligheter som inte har någon egen vattentäkt kan ibland förses med vatten från ett allmänt distributionsnät. I Vaxholms kommun finns nära ett 30-tal samfälligheter som får sitt vatten från Görvälnverket i Järfälla kommun vilket ägs och drivs av kommunalförbundet Norrvatten AB. Behandlat dricksvatten distribueras vidare av Norrvatten AB. I Vaxholms kommun är Vaxholmsvatten AB/ Roslagsvatten AB VA-huvudman och förvaltar kommunens allmänna VA-anläggning. Roslagsvatten AB levererar vatten till vattenkonsumenter som är anslutna till det allmänna VA-nätet i Vaxholms kommun, men bolaget levererar även dricksvatten till nämnda samfälligheter. Vattenverket behandlar (renar) det så kallade råvattnet från vattentäkten (i detta fall Mälaren) för att åstadkomma ett kvalitetsmässigt bra dricksvatten sett ur såväl kemisk som ur mikrobiologisk synvinkel. Kan då dricksvattensamfälligheterna slå sig till ro med att de har ett dricksvatten av god kvalitet? SRMH bedriver kontroll och tillsyn av dricksvattensamfälligheterna och deras distributionsanläggningar. SRMH har gjort sina första pilotinspektioner hos samfälligheterna och uppmärksammat ett antal förmodade brister med vissa rutiner och installationer. I forskningsfältet kring distributionsanläggningar för dricksvatten studeras bland annat faktorer som påverkar mikrobiologisk förekomst och tillväxt i distributionsanläggningar. Mot bakgrund av utvalda delar ur detta forskningsfält har jag skapat ett analytiskt ramverk för att söka värdera mikrobiologiska risker i samfälligheternas distributionsanläggningar. Förutom detta görs några typer av mikrobiologiska analyser för att jämföra med uppskattad risk. Förutom protokoll från SRMH:s inspektioner av samfälligheterna görs små intervjuer av vattenkonsumenter och samfällighetsansvariga. För att se var eventuella kvalitetsproblem uppstår används sekundärdata från Norrvatten som beskriver kvalitet efter vattenverkets behandling och kvalitet vid ett vattentorn på ”halva vägen” samt vid en referenspunkt i Vaxholm. Relevant dricksvattenjuridik studeras också för att ta reda på vem som ansvarar för vad samt för att se vilka kvalitetskrav som är relevanta avseende samfälligheterna. Resultatet antyder försiktigt att riskerna men även vattentemperaturen samt den mikrobiologiska vattenkvaliteten (odlingsbara mikroorganismer) i undersökningen till viss del skiljer mellan olika typer av samfälligheter. För samfälligheter med året-runt-vatten verkar problemen vara mindre, medan för samfälligheter som endast har sommarvatten verkar det finnas fler risker. Det senare verkar även gälla för samfälligheter där fritidsbostäder ingår. Skillnader i antal långsamväxande mikroorganismer mellan olika samfällighetstyper är dock mer osäkra. Kvalitetsreglerna avseende mikrobiologi i samfällighetsnätet och i det allmänna nätet styrs av livsmedelsverkets föreskrifter och EU:s dricksvattendirektiv och alla parter måste försäkra sig om att kvalitetskraven uppfylls inom respektive distributionsnät. Återströmning av vatten från samfälligheter till den allmänna distributionsanläggningen verkar inte kunna regleras av lagen om allmänna vattentjänster och därmed ej heller av det lokala regelverket ABVA för Vaxholm. Enligt min tolkning av regelverket är respektive ägare av distributionsnäten ansvariga för om kvaliteten påverkas i det egna nätet när/om återströmning sker från mottagande part. I diskussionsdelen görs även jämförelser avseende temperatur och mikrobiologiska parametrar mellan de olika typerna av studerade samfälligheter och Norrvattens perifera kommuner för att se om det finns några skillnader. / Continuous access to healthy, clean and good-tasting drinking-water is perceived as obvious for many people in Sweden. The total regeneration of water is currently not a problem in Sweden if uneven distribution and local quality problems are not accounted for. Many regions are supplied with drinking water from one of Sweden’s around 2000 water treatment plants. Other water consumers get their water from private wells, while others get water access via community-owned distribution systems. Sometimes communities that do not have their own water supply can get water supply through a public distribution system. In the municipality of Vaxholm almost 30 small communities get their water from the water treatment plant (WTP) Görvälnverket, which is owned and operated by a municipal association called Norrvatten AB. Norrvatten AB redistributes the treated drinking water. In Vaxholm, Roslagsvatten AB is the legal principal of water and sewage. Roslagsvatten AB distributes water to water consumers in the municipality of Vaxholm. The WTP treats (purifies) the surface water from the water source (in this case Mälaren) in order to provide a good quality drinking water seen from both a chemical and microbiological point of view. Under these circumstances, could the water communities be complacent that they have a good quality drinking water? Södra Roslagens Miljö- och hälsoskyddskontor (SRMH) is the local health protection agency responsible for control and enforcement of drinking water communities in Vaxholm. After having performed pilot inspections at the water communities, SRMH drew attention to some assumed risks and deficiencies with routines and water pipe installations. In the drinking water distribution systems research field, factors influencing microbiological presence and growth are investigated. In the view of selected portions from this research field, I have created an analytical framework to be able to evaluate some kind of microbiological risks in the communities’ water distribution systems. Besides this, some microbiological analyzes are made to compare with assessed risk. In addition to studied protocols from inspections of the communities, some minor interviews are made with water consumers and persons responsible for plumbing in the communities. To assess whether potential quality problems occur, secondary historical quality analysis data from Norrvatten AB is used. Quality data from directly after treatment at the WTP, from a water tower “halfway” to Vaxholm, and from a reference location in Vaxholm is used. Swedish and European Union legal framework of relevance regarding drinking water is studied to find out relevant legal quality requirements with regards to the communities. The result gently suggests that identified risks but also water temperature and investigated microbiological quality (culturable microorganisms; HPC counts, 22 °C, 3 days) in the study to some extent differ between different types of communities. For communities with full-year water supply, the problems seem to be less. On the contrary, for communities with supply only during summer, problems seem to be greater. Problems also seem to exist for communities where holiday residences exist. Differences in the number of slower growing microorganisms (HPC counts, 22 °C, 7 days) between community types is more uncertain. The microbiological quality of drinking water is regulated by Swedish national regulations and by European Union’s drinking water directive. All parties must ensure that quality standards are met in each distribution network. Backflow of water from communities’ distribution networks does not seem to be regulated by the Swedish law on public water services and thus neither by the local regulatory called “ABVA” for Vaxholm. According to my interpretation of the regulations, the respective owners of the distribution networks are responsible for if quality is adversely affected in its own network if backflow occurs from the receiving party. In the discussions chapter, temperature and HPC counts are compared between studied communities and Norrvatten’s peripheral municipalities to assess if differences exist.

Water distribution systems convey drinking water from treatment plant and make available to consumers’ taps. It consists of essential components like pipes, valves, pumps, tanks and reservoirs etc. The main concern in the working of a water distribution system is to assure customer demands under a choice of quantity and quality throughout the complete life span for the probable loading situations. However, in some cases, the existing infrastructure may not be adequate to meet the customer’s requirements. In such cases, system modeling plays an important role in proper management of water supply systems. In present scenario, modeling plays a significant task in appropriate execution of water distribution system. From the angle of taking management decisions valve throttling control and pumps speed control are very important. These operational problems can be addressed by manual control or by automatic control. The problem is the use of manual controls that slow down the effectiveness of the system. It reduces the efficiency of operation of valve or pump. To improve the efficiency of such water distribution systems, an automatic control based technology has been developed that links the operation of the variable speed pump control or valve throttling control. By employing an automatic control, the pump can adjust its speed at all times to meet the actual flow requirements of each load served. In case of real system design Simulink is the most widely used tool. Commercial software package Matlab/Simulink used for creation of WDS model. The goal was to produce a model that could numerically analyze the dynamic performance of a water distribution system. A Comparison of single platform methodology (Simulink based control) and double platform methodology (Matlab and EPANET based control) has been done. Nonlinear Dynamic Inversion (DI) Control system model is developed for WDS model in Matlab/Simulink environment. Controller gain parameters are the very important value in control prospective. If the controller gain parameters are chosen incorrectly, the controlled process input can be unstable, i.e. its output diverges, with or without oscillation Tuning is the adjustment of control parameters (gains) to the optimum values for the desired control response. There are several methods for tuning controller like manual tuning (Trial and error procedure), Ziegler-Nichols method, Output Constraint Tuning (OCT) etc. Establishment of a pump operational policy by which all the reservoirs can be fed simultaneously to meet their requirements without creating undue transients. Tune the gain of DI controllers by different tuning methods and evaluate the best tuning method on the basis of controller performance. Development of meaningful additional objective is search of lower bound pump speed on the basis of control time or settling time. To bring the pump speeds in feasible range, application of constraint in pumps speed is introduced. The magnitude of constraints can be found using Monte Carlo methods. Monte Carlo methods are frequently used in simulating physical and mathematical systems. This method may be the most commonly applied statistical method in engineering and science disciplines. Another benefit is providing increased confidence that a model is robust using Monte Carlo testing. Model development for generalized control system for water distribution network provides the simplification needed for the simulation of large systems. Model development is based on the study of symmetric and non symmetric small, irregular networks, as well as large, regular and open bifurcating water distribution system. The problem considered in this section is that of flow dynamics in simple to complex, regular network which bifurcates in the form of a branching tree. In addition the control application of the flow network is investigated using valves as the manipulated variables to control branch flow rates. Communication between the network hydraulics coming from EPANET and control algorithm develop on Matlab (Programming Language) can be generalized with the help of development of general purpose control algorithm model.

This thesis concerns monitoring in Middle- and Low-Voltage distribution systems penetrated by distributed generation. Monitoring itself means measuring voltages and power flows and sending relevant data to the supervisory system. The first part of the thesis describes distribution systems with differences between individual voltage levels. The following chapter is focused on consequences of high share of renewable energy sources in distribution systems. Most of the problems are partially resolved by technical conditions for connection of the new power sources. However, difficulties with voltage regulation and uncontrolled power flows to higher voltage levels remain. These are the reasons for measuring voltages and currents in medium voltage networks. Second to last subhead of this chapter is dedicated to possible benefits of monitoring. The fourth part of the thesis deals with voltage and current sensors with their advantages and disadvantages. The best suitable devices are chosen in the end of the chapter. It is crucial to mention that sensors are only part of measuring system. Analog outputs from current or voltage transformers need to be converted to digital signal and further processed. After that required quantities are finally sent. Properties of these circuit cards are described in the sixth chapter. Following part aims to define a certain key that will determine the suitable locations for installation of the measurement. The final part of the thesis compares measured voltages and power flows from real 22 kV network with calculated values from computer program PAS DAISY Bizon.

Os geradores distribuídos em sistemas de distribuição de energia elétrica devem ser desconectados em eventos de ilhamento, que ocorrem quando parte da rede elétrica torna-se eletricamente isolada da concessionária e o subsistema isolado continua a ser energizado pela geração distribuída. A proteção anti-ilhamento deve detectar tal condição operativa, porém pode não atuar em condições de pequenos desbalanços entre carga e geração, ou atuar incorretamente para eventos de outra natureza. Assim, um ajuste adequado dessa proteção deve desconectar o gerador rapidamente quando detecta o ilhamento e, simultaneamente, deve ser imune a eventos como curtos-circuitos e chaveamentos de carga, por exemplo. Esta pode ser uma tarefa muito difícil face às variações de carga e diferentes eventos de não ilhamento que podem ocorrer no sistema de distribuição. Portanto, nesta tese são propostas metodologias de ajuste das funções de proteção anti-ilhamento de sub/sobrefrequência, taxa de variação de frequência, salto de vetor e sub/sobretensão, que são técnicas convencionalmente utilizadas para a detecção de ilhamento de geração distribuída. O objetivo das metodologias é maximizar a detecção de ilhamento e minimizar a atuação incorreta, e são considerados cenários com múltiplos geradores distribuídos de diferentes tecnologias. Inicialmente, são explorados os principais fatores que afetam as proteções, tais como distribuição das cargas, fator de potência e desequilíbrio das cargas. Esta análise permite identificar os casos mais difíceis de detecção de ilhamento. Como segunda contribuição, foi proposta a metodologia de análise gráfica denominada Mapa de Ajustes, cuja eficácia foi comprovada por meio de casos de teste, mostrando ser capaz de melhorar a sensibilidade da proteção anti-ilhamento e minimizar atuação incorreta. Na sequência, é apresentado um método automático para ajuste e bloqueio de tensão e outro baseado em proteção adaptativa para ajuste das funções de proteção. Ambos são baseados na metodologia de mapa de ajustes. Os resultados indicam que é possível melhorar a detecção de ilhamento e diminuir a atuação incorreta quando utilizadas as metodologias propostas. / Distributed generators in power distribution systems must be disconnected after an islanding event, which occurs when part of the power grid becomes electrically isolated from the utility and the isolated subsystem continues to be energized by the distributed generation. The antiislanding protection has to detect such operating condition, which may fail for critical loading conditions, or operate incorrectly for events of other nature than islanding. Therefore, an appropriate protection setting should quickly disconnect the generator when an islanding event is detected, and simultaneously, must be immune to events such as short circuits and load switches. This can be a very difficult task due to load variations and different nonislanding events that may occur in the distribution system. Therefore, in this thesis is proposed methodologies to adjust the anti-islanding protection functions of under/overfrequency, rate of change of frequency, vector surge and under/overvoltage, which are techniques conventionally used for islanding detection of distributed generation. The methodologies goals are to maximize the performance of the anti-islanding protection and minimize the incorrect operation to events of other nature, and scenarios with multiple distributed generators of different technologies are considered. At first, the main factors that affect the frequency and voltage-based protection will be explored, such as load distribution, power factor and unbalanced loads. This analysis aims to identify the most critical cases of islanding detection. The second contribution of this thesis is the Setting Map methodology, which is a graphical analysis whose effectiveness has been proved by case studies, showing to be able to improve the sensitivity of anti-islanding protection, minimizing the chances of incorrect operation. In sequence, is presented an automatic method to adjust the protection functions and voltage blocking and other based on adaptive protection. Both methods are based on the Setting Map methodology. The results indicate that it is possible to improve the islanding detection and reduce the incorrect actuation when it is used the proposed methodologies.

Este trabalho apresenta uma metodologia para alocação eficiente de dispositivos indicadores de faltas em sistemas de distribuição de energia elétrica. São avaliadas como as principais variáveis que influenciam na quantificação da potencialidade para instalação de dispositivos indicadores de faltas se comportam ao longo do tronco principal dos alimentadores de distribuição de energia elétrica. Como metodologia, empregou-se sistemas de inferência fuzzy para quantificar a referida potencialidade a partir das variáveis avaliadas. Resultados com dados reais destacam também a eficiência da metodologia proposta para quantificar e avaliar a rede de dispositivos indicadores já existentes em alimentadores. / This work presents a methodology for efficient allocation of fault indicator devices in electric power distribution systems. The behavior of the main variables that influence in the quantification of the potentiality for installation of fault indicator devices were analyzed taking into account the feeder length. In methodology terms, fuzzy inference systems were used to quantify this potentiality from the analyzed variables. Results with real data have also highlighted the efficiency of the proposed methodology to quantify and to evaluate the fault indicator device network already existent in power distribution feeders.

Neste trabalho é proposta uma modelagem matemática para a otimização do problema de corte de carga em sistemas de distribuição de energia elétrica radiais. O problema de corte de carga consiste em uma estratégia de reconfiguração topológica da rede elétrica para interrupção do fornecimento de energia elétrica. O objetivo principal é desligar a quantidade mínima de carga do sistema, de forma a manter restrições físicas e operacionais dentro dos limites da rede elétrica. Um segundo objetivo é alterar o mínimo possível a estrutura topológica inicial do sistema. Para isso, é feita a minimização de chaveamentos. Inicialmente foi modelado como uma programação não-linear inteira mista, e transformado em uma programação cônica de segunda ordem inteira mista, que pode ser resolvida de forma eficiente usando vários solver comerciais. O modelo matemático foi implementado dentro do ambiente de programação matemática GAMS e resolvido utilizando o solver comercial CPLEX. Testes foram realizados no sistema de distribuição de 53 barras. Os resultados encontrados evidenciam a consistência e a eficiência da modelagem proposta neste trabalho. / This research proposed a mathematical model to optimize the load shedding problem in radial distribution power systems. The load shedding problem consists in a topological reconfiguration strategy of the power grid in order to interrupt the power supply. The main goal is to disconnect the minimum amount of system loads while respecting the physical and operational restrictions of the grid. The second goal of this research was to modify as little as possible the initial topological structure of the system. To achieve this, a switching minimization was performed. First, the problem was modeled as a mixed integer nonlinear programming, and then it was transformed into a mixed integer second order cone programming using various commercial solvers. The mathematical model was implemented in the mathematical programming environment GAMS and solved using the CPLEX commercial solver. Tests were performed at the 53 nodes distribution system. The test results showed the consistency and efficiency of the model proposed in this dissertation.

Este trabalho tem por objetivo apresentar uma metodologia para localização e proposição de reforços no sistema de distribuição de energia elétrica através de programação linear, PL, e algoritmo genético, AG. A técnica de PL utilizada para a localização de pontos de reforços e, principalmente, novas subestações de distribuição, é baseada no algoritmo de ?out-of-kilter?, um conhecido algoritmo de transporte. A seleção de melhores alternativas é solucionada através do AG, que permite a modelagem de redes com proporções reais e possibilita a obtenção de resultados em tempos de execução compatíveis para aplicação de atividades em planejamento de sistemas de distribuição de energia. O modelo de algoritmo proposto aloca automaticamente novos reforços, como o recondutoramento de trechos da rede e a expansão de subestações existentes, complementando os reforços candidatos, novas subestações e novos alimentadores, propostos previamente pelo modelo de PL. A metodologia proposta é aplicada à resolução de uma rede de distribuição real, possibilitando a análise da potencialidade que esta modelagem pode oferecer. / This dissertation presents a methodology for the allocation and proposal of new reinforcements in electric distribution systems through linear programming (LP) and genetic algorithm (GA). The linear programming technique used for the allocation of new reinforcements, namely new distribution substation locations, is based on the ?out-of-kilter? algorithm, a well known transport algorithm. The selection of alternatives, determined by technical and economical criteria, is carried out through a genetic algorithm that allows the modeling of real sized distribution networks and makes possible the attainment of results in compatible execution times for distribution network planning. The proposed model places new reinforcements automatically, as it is the case of cable resizing in distribution lines and the expansion of existing substations, complementing the new substations and new feeders proposed by the linear programming model. The proposed methodology is applied to the solution of a real distribution network, showing the potential applications of the models.

Este trabalho tem por objetivo apresentar uma metodologia para localização e proposição de reforços no sistema de distribuição de energia elétrica através de programação linear, PL, e algoritmo genético, AG. A técnica de PL utilizada para a localização de pontos de reforços e, principalmente, novas subestações de distribuição, é baseada no algoritmo de ?out-of-kilter?, um conhecido algoritmo de transporte. A seleção de melhores alternativas é solucionada através do AG, que permite a modelagem de redes com proporções reais e possibilita a obtenção de resultados em tempos de execução compatíveis para aplicação de atividades em planejamento de sistemas de distribuição de energia. O modelo de algoritmo proposto aloca automaticamente novos reforços, como o recondutoramento de trechos da rede e a expansão de subestações existentes, complementando os reforços candidatos, novas subestações e novos alimentadores, propostos previamente pelo modelo de PL. A metodologia proposta é aplicada à resolução de uma rede de distribuição real, possibilitando a análise da potencialidade que esta modelagem pode oferecer. / This dissertation presents a methodology for the allocation and proposal of new reinforcements in electric distribution systems through linear programming (LP) and genetic algorithm (GA). The linear programming technique used for the allocation of new reinforcements, namely new distribution substation locations, is based on the ?out-of-kilter? algorithm, a well known transport algorithm. The selection of alternatives, determined by technical and economical criteria, is carried out through a genetic algorithm that allows the modeling of real sized distribution networks and makes possible the attainment of results in compatible execution times for distribution network planning. The proposed model places new reinforcements automatically, as it is the case of cable resizing in distribution lines and the expansion of existing substations, complementing the new substations and new feeders proposed by the linear programming model. The proposed methodology is applied to the solution of a real distribution network, showing the potential applications of the models.

Neste trabalho é proposta uma modelagem matemática para a otimização do problema de corte de carga em sistemas de distribuição de energia elétrica radiais. O problema de corte de carga consiste em uma estratégia de reconfiguração topológica da rede elétrica para interrupção do fornecimento de energia elétrica. O objetivo principal é desligar a quantidade mínima de carga do sistema, de forma a manter restrições físicas e operacionais dentro dos limites da rede elétrica. Um segundo objetivo é alterar o mínimo possível a estrutura topológica inicial do sistema. Para isso, é feita a minimização de chaveamentos. Inicialmente foi modelado como uma programação não-linear inteira mista, e transformado em uma programação cônica de segunda ordem inteira mista, que pode ser resolvida de forma eficiente usando vários solver comerciais. O modelo matemático foi implementado dentro do ambiente de programação matemática GAMS e resolvido utilizando o solver comercial CPLEX. Testes foram realizados no sistema de distribuição de 53 barras. Os resultados encontrados evidenciam a consistência e a eficiência da modelagem proposta neste trabalho. / This research proposed a mathematical model to optimize the load shedding problem in radial distribution power systems. The load shedding problem consists in a topological reconfiguration strategy of the power grid in order to interrupt the power supply. The main goal is to disconnect the minimum amount of system loads while respecting the physical and operational restrictions of the grid. The second goal of this research was to modify as little as possible the initial topological structure of the system. To achieve this, a switching minimization was performed. First, the problem was modeled as a mixed integer nonlinear programming, and then it was transformed into a mixed integer second order cone programming using various commercial solvers. The mathematical model was implemented in the mathematical programming environment GAMS and solved using the CPLEX commercial solver. Tests were performed at the 53 nodes distribution system. The test results showed the consistency and efficiency of the model proposed in this dissertation.