Este trabalho apresenta uma metodologia de alocação de dispositivos de proteção e manobra ao longo de alimentadores primários de um sistema de distribuição de energia elétrica, de forma a otimizar a quantidade de consumidores afetados e da energia média não distribuída, na ocorrência de desligamentos provocados por uma falha. Na alocação dos dispositivos, utiliza-se um algoritmo matemático que considera vários parâmetros envolvidos no fenômeno, que explicam o mérito de cada alternativa possível, ponderando as variações de benefício. Além de indicar os locais adequados para instalação dos dispositivos de proteção e manobra, a metodologia proposta permite a elaboração de regras para auxiliar a priorização de ações de manutenção e para otimizar os investimentos em alimentadores. Outro resultado da pesquisa é a relocação de dispositivos de proteção e manobra existentes em alimentadores, considerando o seu reposicionamento para melhorar o desempenho em face de faltas que provocam interrupções e portanto diminuindo os indicadores FEC frequência média de interrupção de fornecimento e a END pela energia média não distribuída.Com o objetivo de comprovar a eficácia da metodologia proposta, desenvolveu-se uma ferramenta para sua operacionalização e posterior aplicação com sucesso, em um Estudo de Caso real de uma Concessionária brasileira. / This paper presents a methodology for allocation of protection and switching devices along primary feeders of a system for electricity distribution in order to optimize both the number of affected consumers and the average amount of energy that is not supplied, in case of interruptions caused by a failure. For the allocation of the devices it is used a mathematical algorithm that considers various parameters involved in the phenomenon, explaining the relevance of each possible alternative and pondering benefit variations. Besides indicating the adequate places to install the protection and switching devices, the proposed methodology allows elaborating roles that help taking prior actions to maintain and optimize the investments in feeders. Other aspect of the research is the relocation of protection and switching devices that exist in the feeders, considering their replacing in order to enhance the performance in the occurrence of failures that cause interruptions and so, reducing the FEC indicators supplying interruption medium frequency and the END (Energy not supplied). Aiming to prove the effectiveness of the proposed methodology, it was developed a tool for its operation and subsequent successful application in a study case, that represents a real situation of a Brazilian electrical power retailer company.

O dimensionamento otimizado de sistemas de distribuição de águas tem originado centenas de trabalhos científicos nas últimas quatro décadas. Vários pesquisadores têm buscado encontrar uma metodologia capaz de dimensionar essas redes considerando diversos aspectos e incertezas características desse tipo de projeto. No entanto, os resultados da maioria das metodologias desenvolvidas não podem ser aplicados na prática. O objetivo deste trabalho é elaborar uma metodologia de dimensionamento de redes de distribuição de água considerando um enfoque multiobjetivo. A metodologia desenvolvida considera três aspectos referentes ao projeto desses sistemas: custo; confiabilidade e perdas por vazamentos. Para tanto, empregou-se um método de otimização multiobjetivo baseado em algoritmos genéticos para a geração do conjunto de soluções não-dominadas e um método multicriterial para escolha da alternativa final. Para representar os objetivos do problema, foram testadas nove funções: custo, vazamentos, entropia, resiliência, tolerância à falha, expansibilidade, efeito do envelhecimento e resilientropia, sendo que sete destas são específicas para a representação da confiabilidade. Para se avaliar as alternativas geradas foi desenvolvido um modelo de análise hidráulica que fosse capaz de trabalhar com vazamentos e com demandas dependente da pressão. Os métodos escolhidos foram o Híbrido de Nielsen e o Gradiente. Das funções testadas, a resilientropia, proposta originalmente neste trabalho, foi a que melhor se ajustou ao conceito formal de confiabilidade, representado pela função tolerância. Os resultados encontrados pela metodologia mostraram-se promissores, uma vez esta foi capaz de encontrar redes eficientes ao final das simulações. / The topic \"Optimized design of water distribution systems\" has generated hundreds of scientific publications in the last four decades. Several researchers have searched for a technology which would take into account a variety of aspects and uncertainties innate to the design of such networks. However, the results of most methodologies developed are not practical. The objective of this work is to develop a methodology for water distribution systems design that has a multi-objective focus. The methodology developed focuses in three aspects of the design of such systems: cost, reliability and losses by leaking. A multiobjective optimization method based on generic algorithms, generating a set of non-defined solutions, and a multi-criteria method for choosing the final alternative, was employed. Nine functions representing the objectives of the problem (method) were tested: cost, leakages, entropy, resilience, failure tolerance, expansibility, aging effect and resilienthropy, seven of which are specific to representing reliability. In order to evaluate the generated alternatives, a hydraulic analysis model, that could handle leakages and pressure dependent demands, was developed. The chosen methods were Nielsen\'s Hybrid, and the Gradient. Of all tested functions, resilientropy, originally proposed in this work, proved to be the one best adjusted to the formal concept of reliability, represented by the tolerance function. The results obtained by this methodology are promising, as they produced efficient distribution networks at the end of the simulations performed.

Driven by economic, technical and environmental factors, the energy sector is currently undergoing a profound paradigm shift towards a smarter grid setup. Increased intake of Distributed and Renewable Generation (DG) units is one of the Smart Grid (SG) pillars that will lead to numerous advantages among which lower electricity losses, increased reliability and reduced greenhouse gas emissions are the most salient. The increase of DG units’ penetration will cause changes to the characteristics of distribution networks from being passive with unidirectional power flow towards Active Distribution Networks (ADNs) with multi-direction power flow. However, such changes in the current distribution systems structure and design will halt the seamless DG integration due to various technical issues that may arise. Voltage and reactive power control is one of the most significant issues that limit increasing DG penetration into distribution systems. On the other hand, the term microgrid has been created to be the building block of ADNs. A microgrid should be able to operate in two modes of operation, grid-connected or islanded. The successful implementation of the microgrid concept demands a proper definition of the regulations governing its integration in distribution systems. In order to define such regulations, an accurate evaluation of the benefits that microgrids will bring to customers and utilities is needed. Therefore, there is a need for careful consideration of microgrids in the assessment, operation, planning and design aspects of ADNs. Moreover, SG offers new digital technologies to be combined with the existing utility grids to substantially improve the overall efficiency and reliability of the network. Advanced network monitoring, two ways communication acts and intelligent control methods represent the main features of SG. Thus it is required to properly apply these features to facilitate a seamless integration of DG units in ADNs considering microgrids. Motivated by voltage and reactive power control issues in ADNs, the concept of microgrids, and SG technologies, three consequent stages are presented in this thesis. In the first stage, the issues of voltage and reactive power control in traditional distribution systems are addressed and assessed in order to shed the light on the potential conflicts that are expected with high DG penetration. A simple, yet efficient and generic three phase power flow algorithm is developed to facilitate the assessment. The results show that utility voltage and reactive power control devices can no longer use conventional control techniques and there is a necessity for the evolution of voltage and reactive power control from traditional to smart control schemes. Furthermore, a probabilistic approach for assessing the impacts of voltage and reactive power constraints on the probability of successful operation of islanded microgrids and its impacts on the anticipated improvement in the system and customer reliability indices is developed. The assessment approach takes into account: 1) the stochastic nature of DG units and loads variability, 2) the special philosophy of operation for islanded microgrids, 3) the different configurations of microgrids in ADNs, and 4) the microgrids dynamic stability. The results show that voltage and reactive power aspects cannot be excluded from the assessment of islanded microgrids successful operation. The assessment studies described in the first stage should be followed by new voltage and reactive power planning approaches that take into account the characteristics of ADNs and the successful operation of islanded microgrids. Feeders shunt capacitors are the main reactive power sources in distribution networks that are typically planned to be located or reallocated in order to provide voltage support and reduce the energy losses. Thus, in the second stage, the problem of capacitor planning in distribution network has been reformulated to consider microgrids in islanded mode. The genetic algorithm technique (GA) is utilized to solve the new formulation. The simulation results show that the new formulation for the problem of capacitor planning will facilitate a successful implementation of ADNs considering islanded microgrids. In the third stage, the SG technologies are applied to construct a two ways communication-based distributed control that has the capability to provide proper voltage and reactive power control in ADNs. The proposed control scheme is defined according to the concept of multiagent technology, where each voltage and reactive power control device or DG unit is considered as a control agent. An intelligent Belief-Desire-Intention (BDI) model is proposed for the interior structure of each control agent. The Foundation for Intelligent Physical Agents (FIPA) performatives are used as communication acts between the control agents. First, the distributed control scheme is applied for voltage regulation in distribution feeders at which load tap changer (LTC) or step voltage regulators are installed at the begging of the feeder. In this case, the proposed control aims to modify the local estimation of the line drop compensation circuit via communication. Second, the control scheme is modified to take into consideration the case of multiple feeders having a substation LTC and unbalanced load diversity. To verify the effectiveness and robustness of the proposed control structure, a multiagent simulation model is proposed. The simulation results show that distributed control structure has the capability to mitigate the interference between DG units and utility voltage and reactive power control devices.

The rapid increase of content delivery over the Internet has lead to the proliferation of content distribution networks (CDNs). Management of CDNs requires algorithms for request routing, content placement, and eviction in such a way that user delays are small. Our objective in this work is to design feasible algorithms that solve this trio of problems. We abstract the system of front-end source nodes and back-end caches of the CDN in the likeness of the input and output nodes of a switch. In this model, queues of requests for different pieces of content build up at the source nodes, which route these requests to a cache that contains the content. For each request that is routed to a cache, a corresponding data file is transmitted back to the source across links of finite capacity. Caches are of finite size, and the content of the caches can be refreshed periodically. A requested but missing item is fetched to the cache from the media vault of the CDN. In case of a lack of adequate space at the cache, an existing, unrequested item may be evicted from the cache in order to accommodate a new item. Every such cache refresh or media vault access incurs a finite cost. Hence the refresh periodicity allowed to the system represents our system cost. In order to obtain small user delays, our algorithms must consider the lengths of the request queues that build up at the nodes. Stable policies ensure the finiteness of the request queues, while good polices also lead to short queue lengths. We first design a throughput-optimal algorithm that solves the routing-placement eviction problem using instantaneous system state information. The design yields insight into the impact of different cache refresh and eviction policies on queue length. We use this and construct throughput optimal algorithms that engender short queue lengths. We then propose a regime of algorithms which remedies the inherent problem of wastage of capacity. We also develop heuristic variants, and we study their performance. We illustrate the potential of our approach and validate all our claims and results through simulations on different CDN topologies.

The performance of Internet-based services depends on many server-side, client-side, and network related factors. Often, the interaction among the factors or their effect on service performance is not known or well-understood. The complexity of these services makes it difficult to develop analytical models. Lack of models impedes network management tasks, such as predicting performance while planning for changes to service infrastructure, or diagnosing causes of poor performance. We posit that we can use statistical causal methods to model performance for Internet-based services and facilitate performance related network management tasks. Internet-based services are well-suited for statistical learning because the inherent variability in many factors that affect performance allows us to collect comprehensive datasets that cover service performance under a wide variety of conditions. These conditional distributions represent the functions that govern service performance and dependencies that are inherent in the service infrastructure. These functions and dependencies are accurate and can be used in lieu of analytical models to reason about system performance, such as predicting performance of a service when changing some factors, finding causes of poor performance, or isolating contribution of individual factors in observed performance. We present three systems, What-if Scenario Evaluator (WISE), How to Improve Performance (HIP), and Network Access Neutrality Observatory (NANO), that use statistical causal methods to facilitate network management tasks. WISE predicts performance for what-if configurations and deployment questions for content distribution networks. For this, WISE learns the causal dependency structure among the latency-causing factors, and when one or more factors is changed, WISE estimates effect on other factors using the dependency structure. HIP extends WISE and uses the causal dependency structure to invert the performance function, find causes of poor performance, and help answers questions about how to improve performance or achieve performance goals. NANO uses causal inference to quantify the impact of discrimination policies of ISPs on service performance. NANO is the only tool to date for detecting destination-based discrimination techniques that ISPs may use. We have evaluated these tools by application to large-scale Internet-based services and by experiments on wide-area Internet. WISE is actively used at Google for predicting network-level and browser-level response time for Web search for new datacenter deployments. We have used HIP to find causes of high-latency Web search transactions in Google, and identified many cases where high-latency transactions can be significantly mitigated with simple infrastructure changes. We have evaluated NANO using experiments on wide-area Internet and also made the tool publicly available to recruit users and deploy NANO at a global scale.

Plug-in hybrid electric vehicles (PHEVs) represent a promising future direction for the personal transportation sector in terms of decreasing the reliance on fossil fuels while simultaneously decreasing emissions. Energy used for driving is fully or partially shifted to electricity leading to lower emission rates, especially in a low carbon intensive generation mixture such as that of British Columbia’s. Despite the benefits of PHEVs for vehicle owners, care will need to be taken when integrating PHEVs into existing electrical grids. For example, there is a natural coincidence between peak electricity demand and the hours during which the majority of vehicles are parked at a residence after a daily commute. This research aims to investigate the incremental impacts to distribution networks in British Columbia imposed by the charging of PHEVs. A probabilistic model based on Monte Carlo Simulations is used to investigate the impacts of uncontrolled PHEV charging on three phase networks in the BC electricity system. A model simulating daily electricity demand is used to estimate the residential and commercial demand on a network. A PHEV operator model simulates the actions of drivers throughout a typical day in order to estimate the demand for vehicle charging imposed on networks. A load flow algorithm is used to solve three phase networks for voltage, current and line losses. Representative three phase networks are investigated typical of suburban, urban and rural networks. Scenarios of increasing PHEV penetration on the network and technological advancement are considered in the absence of vehicle charging control. The results are analyzed in terms of three main categories of impacts: network demands, network voltage levels and secondary transformer overloading. In all of the networks, the PHEV charging adds a large amount of demand to the daily peak period. The increase in peak demand due to PHEV charging increases at a higher rate than the increase in energy supplied to the network as a result of vehicles charging at 240V outlets. No significant voltage drop or voltage unbalance problems occur on any of the networks investigated. Secondary transformer overloading rates are highest on the suburban network. PHEVs can also contribute to loss of transformer life specifically for transformers that are overloaded in the absence of PHEV charging. For the majority of feeders, uncontrolled PHEV charging should not pose significant problems in the near term. Recommendations are made for future studies and possible methods for mitigating the impacts.

Driven by economic, technical and environmental factors, the energy sector is currently undergoing a profound paradigm shift towards a smarter grid setup. Increased intake of Distributed and Renewable Generation (DG) units is one of the Smart Grid (SG) pillars that will lead to numerous advantages among which lower electricity losses, increased reliability and reduced greenhouse gas emissions are the most salient. The increase of DG units’ penetration will cause changes to the characteristics of distribution networks from being passive with unidirectional power flow towards Active Distribution Networks (ADNs) with multi-direction power flow. However, such changes in the current distribution systems structure and design will halt the seamless DG integration due to various technical issues that may arise. Voltage and reactive power control is one of the most significant issues that limit increasing DG penetration into distribution systems. On the other hand, the term microgrid has been created to be the building block of ADNs. A microgrid should be able to operate in two modes of operation, grid-connected or islanded. The successful implementation of the microgrid concept demands a proper definition of the regulations governing its integration in distribution systems. In order to define such regulations, an accurate evaluation of the benefits that microgrids will bring to customers and utilities is needed. Therefore, there is a need for careful consideration of microgrids in the assessment, operation, planning and design aspects of ADNs. Moreover, SG offers new digital technologies to be combined with the existing utility grids to substantially improve the overall efficiency and reliability of the network. Advanced network monitoring, two ways communication acts and intelligent control methods represent the main features of SG. Thus it is required to properly apply these features to facilitate a seamless integration of DG units in ADNs considering microgrids. Motivated by voltage and reactive power control issues in ADNs, the concept of microgrids, and SG technologies, three consequent stages are presented in this thesis. In the first stage, the issues of voltage and reactive power control in traditional distribution systems are addressed and assessed in order to shed the light on the potential conflicts that are expected with high DG penetration. A simple, yet efficient and generic three phase power flow algorithm is developed to facilitate the assessment. The results show that utility voltage and reactive power control devices can no longer use conventional control techniques and there is a necessity for the evolution of voltage and reactive power control from traditional to smart control schemes. Furthermore, a probabilistic approach for assessing the impacts of voltage and reactive power constraints on the probability of successful operation of islanded microgrids and its impacts on the anticipated improvement in the system and customer reliability indices is developed. The assessment approach takes into account: 1) the stochastic nature of DG units and loads variability, 2) the special philosophy of operation for islanded microgrids, 3) the different configurations of microgrids in ADNs, and 4) the microgrids dynamic stability. The results show that voltage and reactive power aspects cannot be excluded from the assessment of islanded microgrids successful operation. The assessment studies described in the first stage should be followed by new voltage and reactive power planning approaches that take into account the characteristics of ADNs and the successful operation of islanded microgrids. Feeders shunt capacitors are the main reactive power sources in distribution networks that are typically planned to be located or reallocated in order to provide voltage support and reduce the energy losses. Thus, in the second stage, the problem of capacitor planning in distribution network has been reformulated to consider microgrids in islanded mode. The genetic algorithm technique (GA) is utilized to solve the new formulation. The simulation results show that the new formulation for the problem of capacitor planning will facilitate a successful implementation of ADNs considering islanded microgrids. In the third stage, the SG technologies are applied to construct a two ways communication-based distributed control that has the capability to provide proper voltage and reactive power control in ADNs. The proposed control scheme is defined according to the concept of multiagent technology, where each voltage and reactive power control device or DG unit is considered as a control agent. An intelligent Belief-Desire-Intention (BDI) model is proposed for the interior structure of each control agent. The Foundation for Intelligent Physical Agents (FIPA) performatives are used as communication acts between the control agents. First, the distributed control scheme is applied for voltage regulation in distribution feeders at which load tap changer (LTC) or step voltage regulators are installed at the begging of the feeder. In this case, the proposed control aims to modify the local estimation of the line drop compensation circuit via communication. Second, the control scheme is modified to take into consideration the case of multiple feeders having a substation LTC and unbalanced load diversity. To verify the effectiveness and robustness of the proposed control structure, a multiagent simulation model is proposed. The simulation results show that distributed control structure has the capability to mitigate the interference between DG units and utility voltage and reactive power control devices.

Water distribution networks are being designed by traditional methods based on rules-of-thumb and personal experience of the designer. However, since there is no unique solution to any network design, namely there are various combinations of pipes, pumps, tanks all of which satisfy the same pressure and velocity restrictions, it is most probable that the design performed by traditional techniques is not the optimum one. This study deals how an optimization technique can be a useful tool for a designer during the design to find a solution. The method used within the study is the partial enumeration technique developed by Gessler. The technique is applied by a commercially available software, i.e. WADISO SA. The study is focused on discrepancies between a network designed by traditional techniques and the same network designed by partial enumeration method. Attention is given to steps of enumeration, which are basically grouping of pipes, candidate pipe size and price function assignments, to demonstrate that the designers can control all the phases of optimization process. In this respect, special attention is given to price functions to show the effect of them on the result. The study also revealed that the cost of fitting materials cannot be included in the price function although it may have significant effect in a system composed of closely located junctions. The results obtained from this study are useful to show that although optimization methods do not provide a definite solution / partial enumeration method can assist designers to select the optimum system combination.

Over the past decades, the concepts and methods for reliability assessment have evolved from analysing the ability of individual components to operate without faults and as intended during their lifetime, into the comprehensive approaches for evaluating various engineering strategies for system planning, operation and maintenance studies. The conventional reliability assessment procedures now receive different perspectives in different engineering applications and this thesis aims to improve existing approaches by incorporating in the analysis: a) a more detailed and accurate models of LV and MV networks and their reliability equivalents, which are important for the analysis of transmission and sub-transmission networks, b) the variations in characteristics and parameters of LV and MV networks in different areas, specified as “generic” UK/Scottish highly-urban, urban, sub-urban and rural network models, c) the relevant requirements for network reliability performance imposed by Regulators on network operators, d) the actual aggregate load profiles of supplied customers and their correlation with typical daily variations of fault probabilities and repair times of considered network components, and e) some of the expected “smart grid” functionalities, e.g., increased use of network automation and reconfiguration schemes, as well as the higher penetration levels of distributed generation/storage resources. The conventional reliability assessment procedures typically do not include, or only partially include the abovementioned important factors and aspects in the analysis. In order to demonstrate their importance, the analysis presented in the thesis implements both analytical and probabilistic reliability assessment methods in a number of scenarios and study cases with improved and more detailed “generic” LV and MV network models and their reliability equivalents. Their impact on network reliability performance is analysed and quantified in terms of the frequency and duration of long and short supply interruptions (SAIFI and SAIDI), as well as energy not supplied (ENS). This thesis addresses another important aspect of conventional approaches, which often, if not always, provide separate indicators for the assessment of system-based reliability performance and for the assessment of customer-based reliability performance. The presented analysis attempts to more closely relate system reliability performance indicators, which generally correspond to a fictitious “average customer”, to the actual “best-served” and “worst-served” customers in the considered networks. Here, it is shown that a more complex metric than individual reliability indicators should be used for the analysis, as there are different best-served and worst-served customers in terms of the frequency and duration of supply interruptions, as well as amounts of not supplied energy. Finally, the analysis in the thesis considers some aspects of the anticipated transformation of existing networks into the future smart grids, which effectively require to re-evaluate the ways in which network reliability is approached at both planning and operational stages. Smart grids will feature significantly higher penetration levels of variable renewable-based distributed generation technologies (with or without energy storage), as well as the increased operational flexibility, automation and remote control facilities. In this context, the thesis evaluates some of the considered smart grid capabilities and functionalities, showing that improved system reliability performance might result in a deterioration of power quality performance. This is illustrated through the analysis of applied automation, reconfiguration and automatic reclosing/remote switching schemes, which are shown to reduce frequency and duration of long supply interruptions, but will ultimately result in more frequent and/or longer voltage sags and short interruptions. Similarly, distributed generation/storage resources might have strong positive impact on system reliability performance through the reduced power flows in local networks and provision of alternative supply points, even allowing for a fully independent off-grid operation in microgrids, but this may also result in the reduced power quality levels within the microgrids, or elsewhere in the network, e.g. due to a higher number of switching transfers and transients.

Orientador: Prof. Dr. Edmarcio Antonio Belati / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Elétrica, 2016. / A inclusão de fontes de geração distribuída (GD) em sistemas elétricos vem crescendo nos últimos anos motivando o uso de fontes de energia alternativas renováveis ao mesmo tempo em que tem aumentado a demanda de energia global. Uma das fontes que tem crescido nos últimos anos ao nível mundial é a energia eólica. Frente à possibilidade de uma situação de escassez de energia elétrica, o aumento no custo da eletricidade e a busca constante das companhias por ter uma operação econômica do sistema elétrico, o estudo do desempenho ótimo da rede é apresentado como um tema importante para os centros de operação das companhias de energia elétrica. Desta forma, os Sistemas Elétricos de Potência (SEP) necessitam de ferramentas rápidas de análise para auxiliar os agentes na tomada de decisões surgindo assim o interesse em desenvolver ferramentas de análise que permitam aos operadores da rede tomarem decisões rápidas em relação às possíveis eventualidades ou variações no comportamento do sistema. O objetivo principal deste trabalho é aplicar análise de sensibilidade de segunda ordem (ASSO) nos sistemas de distribuição com geração eólica para obter um possível ponto de operação ótima de forma rápida após ocorrerem perturbações tanto na geração eólica quanto na carga do sistema. Para tanto foi modelado um Fluxo de Potência Ótimo (FPO) com as características do sistema e com o objetivo de minimizar as perdas de potência ativa, caracterizando assim o caso base (CB) e posteriormente aplicou-se a ASSO à solução encontrada no CB de forma a obter uma resposta rápida e econômica. Vale destacar que para validação da metodologia proposta buscou-se aplica-lo em sistemas de distribuição de energia elétrica. / The inclusion of distributed generation sources (DG) in electrical systems has been growing in recent years encouraging the use of alternative renewable energy sources at the same time it has increased the global energy demand. One of the sources that has grown in recent years worldwide is wind energy. Facing the possibility of energy shortage situation, the increase in the cost of electricity and the constant pursuit of companies to have an economic operation of the electrical system, the study of the network optimal performance is presented as a major issue for the operation centers of electricity companies. Thus, the Electric Power System (EPS) need fast analysis tools to assist agents in decision-making thus resulting interest in developing analysis tools that allow network operators to make quick decisions in relation to the possible eventualities or variations in system behavior. The main objective of this work is to apply analysis of second-order sensitivity (ASOS) in distribution systems with wind generation for an approximate point of optimal operation fastest as possible after disturbances occur both in wind generation, as the system load. For Optimal Power Flow (OPF) with the system's features and with the objective of minimize the loss of active power much was modeled, characterizing the base case (BC) and then applying the ASOS the solution obtained in BC in order to get a quick answer and economic. Note that to validate the proposed methodology we sought to apply it in electric power distribution systems.