Orientador: John Fredy Franco Baquero / Resumo: A presença de Geração Distribuída (GD) no Sistema de Distribuição de Energia Elétrica (SDEE) tem se incrementado nos últimos anos devido a mudanças na regulação e a incentivos governamentais, proporcionando benefícios técnicos e econômicos. Em particular, é esperado que a GD renovável (eólica ou solar) seja integrada adequadamente no SDEE, visando contribuir na redução de emissões de gases de efeito estufa. Entretanto, a presença da GD renovável, junto com suas inerentes incertezas, aumenta a complexidade no planejamento do SDEE. Diante do exposto, neste trabalho propõe-se um modelo de programação estocástica de dois estágios para o problema de planejamento da expansão do SDEE multi-período. As incertezas da geração renovável (associadas à irradiação solar e velocidade do vento) e demanda são representadas por meio de cenários. A função objetivo minimiza o valor presente líquido dos investimentos (subestações, circuitos, e alocação de GD), custo da energia, manutenção e operação, assim como o custo das emissões de CO2. A operação das unidades de GD é representada limitando a potência ativa/reativa que pode ser injetada segundo as curvas de capabilidade e restrições de fator de potência. O modelo proposto foi implementado na linguagem de modelamento AMPL e resolvido com o solver CPLEX. Testes utilizando um SDEE de 24 e 54 nós comprovam a eficiência do modelo. / Abstract: The presence of Distributed Generation (DG) in Electrical Distribution Systems (EDSs) has been increased in recent years due to changes in regulation and government incentives, leading to technical and economic benefits. In particular, renewable DG (wind or solar power) is expected to be properly integrated into the EDS, aiming to contribute to the reduction of greenhouse gas emissions. However, the presence of renewable DG, along with its inherent uncertainties, increases the complexity in the planning of the EDS. In this context, this work proposes a two-stage stochastic programming model for the problem of EDSs expansion planning. The uncertainties of renewable generation (associated with solar irradiation and wind speed) and demand, are represented through scenarios. The objective function minimizes the net present value of investments (substations, circuits, and DG allocation), energy cost, maintenance and operation, as well as the cost of CO2 emissions. The operation of the DG units is represented by limiting the active/reactive power that can be injected according to capability curves and power factor constraints. The proposed model was implemented in the modeling language AMPL and solved with the solver CPLEX. Tests using a 24 and 54-nodes EDS prove the efficiency of the proposed model. / Mestre

With increasing global change pressures such as urbanization and climate change, cities of the future will experience difficulties in efficiently managing scarcer and less reliable water resources. However, projections of future global change pressures are plagued with uncertainties. This increases the difficulty in developing urban water systems that are adaptable to future uncertainty. A major component of an urban water system is the distribution system, which constitutes approximately 80-85% of the total cost of the water supply system (Swamee and Sharma, 2008). Traditionally, water distribution systems (WDS) are designed using deterministic assumptions of main model input variables such as water availability and water demand. However, these deterministic assumptions are no longer valid due to the inherent uncertainties associated with them. Hence, a new design approach is required, one that recognizes these inherent uncertainties and develops more adaptable and flexible systems capable of using their active capacity to act or respond to future alterations in a timely, performance-efficient, and cost-effective manner. This study develops a framework for the design of flexible WDS that are adaptable to new, different, or changing requirements. The framework consists of two main parts. The first part consists of several components that are important in the pre and post--processing of the least-cost design methodology of a flexible WDS. These components include: the description of uncertainties affecting WDS design, identification of potential flexibility options for WDS, generation of flexibility through optimization, and a method for assessing of flexibility. For assessment a suite of performance metrics is developed that reflect the degree of flexibility of a distribution system. These metrics focus on the capability of the WDS to respond and react to future changes. The uncertainties description focuses on the spatial and temporal variation of future demand. The second part consists of two optimization models for the design of centralized and decentralized WDS respectively. The first model generates flexible, staged development plans for the incremental growth of a centralized WDS. The second model supports the development of clustered/decentralized WDS. It is argued that these clustered systems promote flexibility as they provide internal degrees of freedom, allowing many different combinations of distribution systems to be considered. For both models a unique genetic algorithm based flexibility optimization (GAFO) model was developed that maximizes the flexibility of a WDS at the least cost. The efficacy of the developed framework and tools are demonstrated through two case study applications on real networks in Uganda. The first application looks at the design of a centralized WDS in Mbale, a small town in Eastern Uganda. Results from this application indicate that the flexibility framework is able to generate a more flexible design of the centralized system that is 4% - 50% less expensive than a conventionally designed system when compared against several future scenarios. In addition, this application highlights that the flexible design has a lower regret under different scenarios when compared to the conventionally designed system (a difference of 11.2m3/US$). The second application analyzes the design of a decentralized network in the town of Aura, a small town in Northern Uganda. A comparison of a decentralized system to a centralized system is performed, and the results indicate that the decentralized system is 24% - 34% less expensive and that these cost savings are associated with the ability of the decentralized system to be staged in a way that traces the urban growth trajectory more closely. The decentralized clustered WDS also has a lower regret (a difference of 17.7m3/US$) associated with the potential future conditions in comparison with the conventionally centralized system and hence is more flexible.

Outages in the electric grid can be costly for society. Because of this, reliability is one of the parameters used to regulate network companies. Reliability in electrical grids can be measured with SAIDI, system average interruption duration index, which for Fortum Distribution has increased in Stockholm’s distribution network (11 kV) in the early 2000’s. By using outage data for Stockholm from 2011-2013, sets of parameters to be used for reliability calculations in the network information program Tekla NIS were derived. Two different options for investment were then analysed: changing old cables with high fault frequencies, and installing automatic switching in distribution substations. These options were also analysed in a simplified model built in Microsoft Excel. The model calculates the reliability of Stockholm’s distribution network using Markov chains and the network’s average line from a transmission substation’s feeder. The Excel model is faster than Tekla NIS but is limited and less detailed, however the results from Tekla NIS and the Excel model were found to be almost equivalent. The priority for reliability investments in Stockholm should be to change old cables of the type FCJJ since it increases the fault frequencies in the network, while an ageing network decreases the grid fees Fortum Distribution can charge. Simplifications and assumptions, due to insufficient outage data and some problems with Tekla NIS, had to be made when deriving parameters for reliability calculations in both Tekla NIS and the Excel model. However, Tekla NIS can be used to incorporate reliability analysis in network planning, but since Fortum Distribution currently only uses it sparsely, further testing and analysis of the programme is recommended if the usage is to increase. The Excel model can be used for making fast and rough estimates of the result of the two analysed options of investment. / <p>I den tillgängliga fulltexten är tre figurer med tillhörande information i kapitel 2.4 borttagna från originalrapporten efter önskemål från samarbetspartner.</p>

This study gives a description about the development of a computer model, RealPipe, which relates genetic algorithm (GA) to the well known problem of least-cost design of water distribution network. GA methodology is an evolutionary process, basically imitating evolution process of nature. GA is essentially an efficient search method basically for nonlinear optimization cases. The genetic operations take place within the population of chromosomes. By means of various operators, the genetic knowledge in chromosomes change continuously and the success of the population progressively increases as a result of these operations. GA optimization is also well suited for optimization of water distribution systems, especially large and complex systems. The primary objective of this study is optimization of a water distribution network by GA. GA operations are realized on a special program developed by the author called RealPipe. RealPipe optimizes given water network distribution systems by considering capital cost of pipes only. Five operators are involved in the program algorithm. These operators are generation, selection, elitism, crossover and mutation. Optimum population size is found to be between 30-70 depending on the size of the network (i.e. pipe number) and number of commercially available pipe size. Elitism rate should be around 10 percent. Mutation rate should be selected around 1-5 percent depending again on the size of the network. Multipoint crossover and higher rates are advisable. Also pressure penalty parameters are found to be much important than velocity parameters. Below pressure penalty parameter is the most important one and should be roughly 100 times higher than the other. Two known networks of the literature are examined using RealPipe and expected results are achieved. N8.3 network which is located in the northern side of Ankara is the case study. Total cost achieved by RealPipe is 16.74 percent lower than the cost of the existing network / it should be noted that the solution provided by RealPipe is hydraulically improved.

Resumo: Neste trabalho a metaheurística GRASP é utilizada para resolver o problema de reconfiguração de sistemas de distribuição de energia elétrica modelado como um problema de programação não linear binário misto. O objetivo é minimizar as perdas de potência ativa do sistema sujeito a restrições físicas e operacionais do sistema de distribuição. As variáveis binárias do problema representam a abertura e/ou fechamento de chaves de interconexão existentes nos ramos do sistema e as variáveis contínuas representam as tensões nodais e ângulos das tensões nodais. Na metodologia utilizada todas as chaves de interconexão do sistema de distribuição estão fechadas no início do processo e a cada passo da fase construtiva do GRASP um ramo é desconectado do sistema e um fluxo de carga é resolvido. Na fase de melhoria, tendo em vista que a solução da fase construtiva é um sistema radial, foi utilizado a cada iteração um fluxo de carga especializado para sistemas radiais. Para garantir que o sistema de distribuição opere de forma radial, foi introduzido na metodologia de solução uma rotina na qual é verificada a formação de laços e a conectividade do sistema em cada iteração das fases de construção e de melhoria local. São apresentados testes realizados utilizando os sistemas de 14, 33, 84,119 e 136 barras para avaliar a eficiência e robustez da metodologia proposta. Os resultados obtidos foram comparados aos resultados encontrados na literatura com o objetivo de validar a proposta deste trabalho / Abstract: In this work the GRASP is used to solve the problem of reconfiguring systems for electricity distribution modeled as a nonlinear programming problem of binary mixture. The goal is to minimize the power losses of the system subject to physical constraints and operating the distribution system. The problem of binary variables represents the opening and/or closing braces interconnecting branches existing in the system and the continuous variables represent the nodal voltages and angles of nodal voltages. In the methodology used to interconnect all the keys of the distribution system are closed at the beginning of the process and every step of the constructive phase of GRASP a branch is disconnected from the system and a load flow is solved. In the improvement phase, given that the solution of the constructive phase is a radial system was used at each iteration a load flow for radial systems specialist. To ensure that the distribution system operates in a radial manner, was introduced into the solution methodology is a routine in which verified the formation of linkages and connectivity of the system in each iteration of the phases of construction and local improvement. Tests are presented using the systems 14, 33, 84, 119 and 136 bus to evaluate the efficiency and robustness of the proposed methodology. The results were compared to results from the literature in order to validate the proposal of this work / Orientador: Rubén Augusto Romero Lázaro / Coorientador: Marina Lavorato de Oliveira / Banca: Marcos Julio Rider Flores / Banca: Eduardo Nobuhiro Asada / Mestre

A continuidade no fornecimento de energia elétrica a clientes é um objetivo constante das distribuidoras de energia, as quais estão constantemente buscando desenvolver soluções tecnológicas a fim de melhorar o desempenho das redes de distribuição. Com o crescimento das cargas eletrônicas e o expressivo aumento dos dispositivos automáticos nas redes, surge uma nova forma de analisar a rede de distribuição sob o aspecto da filosofia da proteção, considerando interrupções sustentadas e momentâneas, sob dois aspectos distintos, o primeiro considera o custo da energia não fornecida sob o período de contingência, enquanto que o segundo refere-se ao impacto do custo social para diferentes classes de clientes, durante o período das interrupções. Desta forma este trabalho propõe o desenvolvimento de uma estratégia de minimização de custos dessas interrupções considerando as características das cargas, bem como o tempo necessário para reinicialização da carga. Para este fim, é aplicado um modelo de programação não-linear, que emprega variáveis binárias para definir a habilitação ou não de curvas rápidas nos religadores e uma abordagem de otimização clássica. Os algoritmos foram desenvolvidos no software Matlab e posteriormente convertido para linguagem GAMS (Generic Algebraic Modeling System). A metodologia foi testada e validada em um alimentador de distribuição real urbano, localizado na região metropolitana de Porto Alegre (RS, Brasil). / Uninterrupted power delivery is a permanent goal of power utilities. One way of attaining this objective is constantly investing in technological solutions to improve the performance of distribution networks. With increasing loads, mainly electronic ones, as well as growing insertion of automatic reclosers, the protection philosophy of distribution systems has to be rethought taking into account temporary and permanent interruptions. In this work, we propose a strategy to minimize the cost of interruptions taking into account the load characteristics and the time required to restart the load. This is achieved by deriving a mixed integer nonlinear programming model. The proposed model uses binary variables to define if the instantaneous characteristic of the recloser should be enabled and a classical explicit mathematical optimization approach. The algorithms were developed with Matlab software and the conversion was made to a General Algebraic Modeling System (GAMS). The applicability of the proposed methodology is tested in an actual feeder from Porto Alegre.

Our society is heavily dependent on commodities, as water and electricity, supplied to final users by engineered systems, which are known as critical infrastructures. In such context, the understanding of how such systems handle damaging events is an important aspect and is a current concern of researchers, public agents, and society. How much of performance a system loses due to damages is related to its vulnerability, and the ability to absorb and recover successfully from damages is its resilience. In this study, approaches to assess the vulnerability and resilience of power distribution systems by evaluating dynamic features, as the processes of failure and repair, and system reconfiguration for vulnerability, and the effects of extreme weather scenarios for resilience together with the processes of failure of repair are presented. Such approaches were applied on systems previously presented in the literature, and also on a Brazilian power distribution system. A Monte Carlo simulation was applied to evaluate this systems, models for time-to-failure and time-to-repair under different circumstances were obtained from historical data, and a method to use the models of time-to-failure during the vulnerability analysis was introduced. In addition, an assessment of the impact of reconfiguration capability on vulnerability is also carried out, and a resilience assessment under different climate scenarios has been developed. The time-to-failure and repair models highlighted how external factors modifies the Brazilian system failure and repair dynamics, the use of time-to-failure models during vulnerability analysis showed that the consideration of the failure dynamic of the types of elements give different results, and the time domain allows new analysis\' perspectives. The investigation indicated that the vulnerability reduction due to reconfiguration is affected by the number of switches and also the maximum load capacity of the distribution system feeders. The resilience assessment showed that for structural connectivity, larger distribution networks are less resilient, while for electricity delivery, a set of features, related with the topological and electrical organization of such networks, seems to be associated with the network service resilience, such information is useful for system planning and management. The dynamics evaluated in this study are relevant to vulnerability and resilience of such systems, and also to other critical infrastructures. Moreover, the developed approaches can be applied to other systems, as transportation and water distribution. In future studies, other power distribution systems features, as distributed generation and energy storage, will be considered in both, vulnerability and resilience analysis. / Nossa sociedade é altamente dependente de commodities, como água e eletricidade, fornecidas para os usuários por sistemas de engenharia, conhecidos como infraestruturas críticas. A compreensão de como tais sistemas lidam com eventos prejudiciais é uma preocupação atual de pesquisadores, agentes públicos e sociedade. A perda de desempenho de um sistema devido a danos é relacionada à sua vulnerabilidade, e a capacidade de absorver e se recuperar dos danos é a resiliência. Neste estudo, são apresentadas abordagens para avaliar a vulnerabilidade e resiliência de sistemas de distribuição de energia considerando características dinâmicas, como os processos de falha e reconfiguração do sistema, para a vulnerabilidade, e os efeitos de climas extremos na resiliência com os processos de falha e reparo. Tais abordagens foram aplicadas em sistemas previamente apresentados na literatura, e também em um sistema brasileiro. Simulação de Monte Carlo foi utilizada para avaliar as dinâmicas de falha e reparo do sistema utilizando de modelos obtidos a partir de dados históricos, e um método para usar os modelos de tempo-até-falha durante a análise de vulnerabilidade também foi apresentado. Além disso, uma avaliação do impacto da dinâmica de reconfiguração na vulnerabilidade foi realizada e uma avaliação de resiliência sob diferentes cenários climáticos foi desenvolvida. Os modelos tempo-para-falha e reparo destacaram como fatores externos modificam as dinâmicas de falha e reparo do sistema brasileiro, o uso de modelos de confiabilidade na análise de vulnerabilidades mostrou que a consideração dos diferentes tipos de elementos geram resultados diferentes e o domínio de tempo permite novas perspectivas de análise. A investigação da reconfiguração indicou que a redução da vulnerabilidade devido à reconfiguração é afetada pelo número de chaves e também pela máxima capacidade de carga dos alimentadores do sistema de distribuição. A avaliação de resiliência mostrou que, para conectividade estrutural, redes de distribuição maiores são menos resilientes, enquanto que para fornecimento de energia, um conjunto de características, relacionados com a organização topológica e elétrica dessas redes parece ser associado à resiliência do serviço, informação útil para o planejamento. As dinâmicas avaliadas neste estudo são relevantes para a vulnerabilidade e resiliência de tais sistemas, e também para outras infraestruturas críticas. Além disso, essas abordagens podem ser aplicadas a outros sistemas, como transporte e distribuição de água. Em estudos futuros, outras características de sistemas de distribuição de energia, como geração distribuída e armazenamento de energia, serão consideradas nas análises de vulnerabilidade e resiliência.

O sistema elétrico brasileiro possui atualmente níveis de perdas elétricas da ordem de 15%. Destes, aproximadamente a metade são provenientes das chamadas perdas comerciais (PC) que ocorrem nos sistemas de distribuição. As PC são a soma de toda energia não faturada pelas distribuidoras, á exceção das perdas técnicas. As suas causas mais frequentes são os furtos de energia elétrica, fraudes e defeitos em medidores. Os custos provenientes dessas perdas são normalmente repassados pelas distribuidoras aos consumidores regulares. No entanto, novas regulamentações do regulador brasileiro do sistema elétrico, a Agência Nacional de Energia Elétrica (ANEEL), impõem limite a esse repasse, o que cria nas concessionárias um maior incentivo para o seu combate. Entre as metodologias empregadas para a mitigação de PC, tem sido destacadas na literatura aquelas baseadas na análise das bases de dados de clientes das empresas distribuidoras com o objetivo de reconhecer padrões de clientes irregulares. Neste contexto, neste trabalho é proposto e desenvolvido um sistema de combate a PC baseado no classificador supervisionado Floresta de Caminhos Ótimos (Optimum-Path Forest, OPF). São propostas a utilização de dados categóricos e a normalização de dados como modificações nos métodos encontrados na literatura. Os testes com o sistema desenvolvido são aplicado a uma base de dados sintetizada a partir de clientes residenciais, diferentemente de trabalhos em que se utilizaram dados de consumidores comerciais e industriais. Os resultados mostram que as modificações propostas podem melhorar o desempenho do OPF. O comparativo com outros métodos de classificação reafirma a eficiência do OPF mas contesta alguns resultados presentes na literatura. / The Brazilian electric power system has about 15% of losses. About a half of this amount is due to the so called commercial losses. The commercial losses are the sum of the unbilled energy less the technical losses. The commercial losses are mainly caused by electricity theft, frauds in electricity meters and electricity meter failure. The financial costs caused by these losses are included in the electricity bill, paid by the regular consumers. New regulations approved by the Brazilian regulatory agency for the electric system create a limit for this, which stimulates the investments in commercial loss mitigation by distribution companies. Among the methods used to mitigate commercial losses, those based on pattern recognition of irregular consumers within electric companies’ clients’ databases are some of the most promising. In this work, a system for commercial losses mitigation based on the supervised classifier Optimum-Path Forest (OPF) is studied and developed. Categorical data and data normalization are proposed as methods for improving classifier performance. In order to check the system performance, tests are conducted on a database derived from residential consumer data found in the literature, differently from other works which proposed data classification for commercial and industrial consumers only. The results show that using categorical data and normalization may improve OPF performance. Comparing this method with other classifiers confirms OPF’s efficiency but contests some results shown in the literature.

Sistemas de Distribuição de Energia Elétrica (SDEE) estão, pelas próprias condições de funcionamento, sujeitos a perdas de energia e quedas nos níveis de tensão. Uma das formas de reduzir as perdas e ao mesmo tempo melhorar o perfil de tensão do SDEE consiste na utilização de bancos de capacitores e reguladores de tensão ao longo dos alimentadores. Para isto a alocação ótima destes equipamentos torna-se de fundamental importância, logo este trabalho tem por objetivo a utilização de um método quadrático de programação por metas multiobjetivo para a ótima alocação desses equipamentos visando a redução de perdas (meta 1) com o menor custo de investimento (meta 2) sujeito a restrições do fluxo de potência, limites técnicos de operação, mudança no controle dos capacitores chaveados e dos taps dos reguladores de tensão. O constante aumento na penetração da geração distribuída traz novos desafios para o controle e a operação dos SDEE. A metodologia proposta considera os efeitos destas fontes de geração e os seus impactos na alocações ótima dos bancos de capacitores e reguladores de tensão. Com o intuito de resolver o problema de otimização em programas comerciais como Gurobi e Cplex uma metodologia linear de cálculo de fluxo de potência é utilizada. Os algoritmos foram desenvolvidos no software Matlab, e posteriormente foi realizada a conversão para linguagem GAMS (Generic Algebraic Modeling System) para utilização dos solvers na plataforma NEOS (Network Enabled Optimization System). / Power distribution systems (DS) are susceptible to energy loss and voltage drops, mainly because of the way that they are operated and built. One way to minimize system loss and improve the voltage profile of DS is with the use of capacitor banks and voltage regulators (VRs) along the distribution feeders. In this scenario, the optimal placement of these devices becomes crucial. In this paper, a quadratic multi objective goal programming method is proposed to obtain the optimal placement of these devices, where the goals are energy loss (goal 1) and the total investment cost (goal 2). The model is subject to system operation constraints, such as power flow demands, limits of voltages and currents, number of stages of switched capacitors and the tap control of VRs. The increase of distributed generation penetration brings new challenges for control and operation of DS. The proposed methodology considers the effects of these power sources and their impact on optimal allocations of capacitors and VRs. With the aim of solving the optimization problem in commercial programs, a linear power flow is used. The algorithms were developed with Matlab software and the conversion was made to a General Algebraic Modeling System (GAMS) language and solved in the NEOS (Network Enabled Optimization System) platform.

Submitted by Gabriel Figueiredo Puerta (gfpuerta@gmail.com) on 2018-11-12T17:24:33Z No. of bitstreams: 1 diss_Gabriel_Final_real_oficial_.pdf: 2623476 bytes, checksum: a1018496f3944da6d7825e6856e593ac (MD5) / Approved for entry into archive by Cristina Alexandra de Godoy null (cristina@adm.feis.unesp.br) on 2018-11-13T16:56:42Z (GMT) No. of bitstreams: 1 puerta_gf_me_ilha.pdf: 2623476 bytes, checksum: a1018496f3944da6d7825e6856e593ac (MD5) / Made available in DSpace on 2018-11-13T16:56:42Z (GMT). No. of bitstreams: 1 puerta_gf_me_ilha.pdf: 2623476 bytes, checksum: a1018496f3944da6d7825e6856e593ac (MD5) Previous issue date: 2018-08-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho, apresenta-se um modelo matemático especializado para a otimização do problema da restauração de redes de distribuição de energia elétrica radiais quando existem poucas chaves manobráveis. A existência de um número reduzido de chaves seccionadoras na rede de distribuição é uma característica típica de sistemas reais. O problema da restauração de redes de distribuição consiste em obter um plano de restauração que restabeleça o máximo possível de cargas presentes na parcela do sistema que foi desenergizada após a ocorrência de uma falta permanente. O plano de restauração deve ser obtido o mais rápido possível. O modelo matemático proposto possui como objetivo maximizar o restabelecimento de energia àqueles setores de carga que estão desenergizados e minimizar o número total de chaveamentos necessários para que a restauração aconteça. O modelo matemático resultante é de programação cônica de segunda ordem inteira mista e é resolvido através de solucionadores comerciais que se baseiam em técnicas de otimização clássicas. Os testes considerando faltas permanentes foram simulados em sistemas de distribuição testes de 53 e 84 barras. Os sistemas foram adaptados e transportados para a problemática do trabalho e os resultados adquiridos qualificam a robustez e a eficácia do modelo matemático especializado proposto para a resolução do problema. / This work proposes an specialized mathematical model for the optimization of the restoration problem in radial electric power distribution systems with few manageable switches. The existence of a reduced number of switches in the distribution systems it’s a typical characteristic of real systems. The restoration problem in radial electric power distribution systems is to obtain a restoration plan that reestablishes the maximum amount of present loads in the system portion that has been de-energized after the occurrence of a permanent fault. The elaboration of the restoration plan must be as soon as possible. The proposed mathematical model aims at maximizing the power re-establishment to the de-energized load sectors and at minimizing the total amount of operated switches that are required for the restoration happen. The resulting mathematical model is a mixed-integer second-order conic programming problem and it’s solved through commercial solves that use classical optimization techniques as base. The tests considering permanents faults were simulated in 84 and 53-bus distribution systems. The systems were adapted and transported to the work’s problematic and the acquired results show the robustness and the effectiveness of the proposed specialized mathematical model for the problem resolution. / CAPES: 001 / FAPESP: 2015/21972-6