Made available in DSpace on 2014-06-11T19:30:51Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-07-30Bitstream added on 2014-06-13T21:01:25Z : No. of bitstreams: 1 rahmani_m_dr_ilha.pdf: 1611068 bytes, checksum: 2b5fe6298f168bf850731b36fc9d3069 (MD5) / O estado da arte em modelagem matemática do problema de planejamento da expansão de sistemas de transmissão (TEP) é analisado nesta tese de doutorado. É proposto um novo modelo linear disjuntivo para o problema TEP baseado no conceito de sistemas de numeração binária para transformar o modelo linear disjuntivo convencional em um problema com um número de variáveis binárias e contínuas muito menores, assim como do número de restrições relacionadas com essas variáveis. Também é usada a fase construtiva da metaheurística GRASP e restrições adicionais, encontradas da generalização do equilibrio de fluxo de potência em uma barra ou conjunto de barras para reduzir o espaço de busca. Os resultados mostram a importância da estratégia de redução do espaço de busca do problema TEP para resolver os modelos de transporte e linear disjuntivo. O problema TEP multiestágio é modelado como um problema de programação linear binária mista e resolvido usando um solver do tipo branch and bound comercial com tempos de processamento relativamente baixos. Outro tópico pesquisado foi a alocação de dispositivos FACTS tais como os capacitores fixos em série (FSCs) para aproveitar melhor a capacidade de transmissão das linhas e adiar ou reduzir o investimento em novas linhas de transmissão em um ambiente de planejamento multiestágio. Assim, pode ser esperado uma excelente relação custo/benefício da integração de dispositivos FSCs no planejamento multiestágio da expansão de sistemas de transmissão. Os resultados encontrados usando alguns sistemas testes mostram que a inclusão de FSCs no problema TEP é uma estratégia válida e efetiva em investimento para as empresas transmissoras e para os responsáveis da expansão nacional do sistema elétrico. / State-of-the-art models for transmission expansion planning problem are provided in this thesis. A new disjunctive model for the TEP problem based on the concept of binary numerical systems is proposed in order to transform the conventional disjunctive model to a problem with many fewer binary and continuous variables as well as connected constraints. The construction phase of a greedy randomized adaptive search procedure (GRASP-CP) together with fence constraints, obtained from power flow equilibrium, are employed in order to reduce search space. The studies demonstrate that the proposed search space reduction strategy, has an excellent performance in reducing the search space of the transportation model and reduced disjunctive model of TEP problem. The multistage TEP problem is modeled as a mixed binary linear programming problem and solved using a commercial branch and bound solver with relatively low computational time. Another topic studied in this thesis, is the allocation of FACTS devices in TEP problem. FACTS devices such as fixed series capacitors (FSCs) are considered in the multistage TEP problem to beter utilize the whole transfer capacity of the network and, consequently, to postpone or reduce the investment in new transmission lines. An excellent benefit-cost ratio can be expected from integration of FSC in multistage transmission expansion planning. The results obtained by using some real test systems indicate that the inclusion of FSCs in the TEP problem is a viable and cost-effective strategy for transmission utilities and national planning bureaus.

Made available in DSpace on 2014-06-11T19:30:51Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-03-25Bitstream added on 2014-06-13T19:06:32Z : No. of bitstreams: 1 santos_db_dr_ilha.pdf: 749223 bytes, checksum: a2917d0d97ef24108b6802f76937b5c1 (MD5) / O problema de planejamento da expansão de sistemas de transmissão de energia elétrica a longo prazo é um importante problema de otimização do campo do planejamento de sistema elétricos de potência. Trata-se de um problema cujo modelo matemático é um problema de programação não linear inteiro misto com a complexidade adicional de que é um problema não convexo e com característica de apresentar o fenômeno da explosão combinatória quando cresce as alternativas de expansão. O processo de resolução consiste basicamente nas escolhas de circuitos, dentro de um conjunto pré-definido, donde o candidato a ser incorporado ao sistema deverá apresentar resultados positivos no que tange a minimização do custo de investimento e operação e, além disso, deve atender a demanda de energia futura ao longo de um horizonte de planejamento com confiabilidade, assumindo como conhecido o plano de geração. Devido a complexidade do problema tem-se tentado aplicar todas as técnicas de otimização para auxiliar na tentativa de resolução. Sendo estas técnicas classificadas em três grandes grupos: técnicas de otimização clássica, técnicas heurísticas e técnicas metaheurísticas. Neste trabalho apresenta-se uma nova forma de resolução, oriunda do grupo , denominada Busca em vizinhança variável (VNS). O VNS é uma metaheurística recente que explora basicamente a ideia de mudança sistemática de estruturas de vizinhança no espaço de soluções durante o processo de busca para encontrar soluções ótimas locais e para sair desses ótimos locais. Esta técnica de solução oferece novas alternativas de solução, comparado com os diversos tipos de metaheurísticas já utilizadas na literatura, apresentando excelentes resultados com baixo esforço computacional. Os algoritmos utilizados são apresentados e detalhados a sua forma de... / The expansion planning problem of the power electrical transmission system to long term is an important problem of optimization of power electrical system fields. It refers to a problem whose mathematical model is a non-linear whole mixed program problem with additional complexity is a non-convex problem and presents the feature of the combinatorial expansion when grows the expansion alternatives. The reduction process is just choices of circuits in a pre-defined array where the candidate, which should be incorporated to the system, should have positive minimization cost of investment and operation and should support the future energy demand along of a reliable horizon of planning to a known generation plan. In the past, many optimization methods were tested to search the best solution due the problem complexity. These methods can be classified by: classical optimization methods, heuristic methods and meta-heuristic methods. However, in this work is presented a new approach of solution based on the method of Variable Neighborhood Search (VNS). The VNS is a modern meta-heuristic uses a systematic change of neighborhood structures over solution space during the search procedure of optimal local solutions and to go out from local optimum. Thus, this approach provides new alternatives of solution in comparison with other meta-heuristic methods previously found at the literature. Additionally, the new approach presents excellent results with low computational cost. In summary, the used algorithms are showed and the adaptation mode to the planning problem of the power electrical transmission system is described. This adaptation considers two traditional mathematical models: Transport and DC models. Lastly, it was performed tests with the bars/paths IEEE system, the bars/paths south Brazilian system and... (Complete abstract click electronic access below)

Orientador: Rubén Augusto Romero Lázaro / Coorientador: Marcos Julio Rider Flores / Banca: José Roberto Sanches Mantovani / Banca: Antonio Cesar Baleeiro Alves / Banca: Sergio Luis Haffner / Banca: Gerson Couto de Oliveira / Resumo: O estado da arte em modelagem matemática do problema de planejamento da expansão de sistemas de transmissão (TEP) é analisado nesta tese de doutorado. É proposto um novo modelo linear disjuntivo para o problema TEP baseado no conceito de sistemas de numeração binária para transformar o modelo linear disjuntivo convencional em um problema com um número de variáveis binárias e contínuas muito menores, assim como do número de restrições relacionadas com essas variáveis. Também é usada a fase construtiva da metaheurística GRASP e restrições adicionais, encontradas da generalização do equilibrio de fluxo de potência em uma barra ou conjunto de barras para reduzir o espaço de busca. Os resultados mostram a importância da estratégia de redução do espaço de busca do problema TEP para resolver os modelos de transporte e linear disjuntivo. O problema TEP multiestágio é modelado como um problema de programação linear binária mista e resolvido usando um solver do tipo branch and bound comercial com tempos de processamento relativamente baixos. Outro tópico pesquisado foi a alocação de dispositivos FACTS tais como os capacitores fixos em série (FSCs) para aproveitar melhor a capacidade de transmissão das linhas e adiar ou reduzir o investimento em novas linhas de transmissão em um ambiente de planejamento multiestágio. Assim, pode ser esperado uma excelente relação custo/benefício da integração de dispositivos FSCs no planejamento multiestágio da expansão de sistemas de transmissão. Os resultados encontrados usando alguns sistemas testes mostram que a inclusão de FSCs no problema TEP é uma estratégia válida e efetiva em investimento para as empresas transmissoras e para os responsáveis da expansão nacional do sistema elétrico. / Abstract: State-of-the-art models for transmission expansion planning problem are provided in this thesis. A new disjunctive model for the TEP problem based on the concept of binary numerical systems is proposed in order to transform the conventional disjunctive model to a problem with many fewer binary and continuous variables as well as connected constraints. The construction phase of a greedy randomized adaptive search procedure (GRASP-CP) together with fence constraints, obtained from power flow equilibrium, are employed in order to reduce search space. The studies demonstrate that the proposed search space reduction strategy, has an excellent performance in reducing the search space of the transportation model and reduced disjunctive model of TEP problem. The multistage TEP problem is modeled as a mixed binary linear programming problem and solved using a commercial branch and bound solver with relatively low computational time. Another topic studied in this thesis, is the allocation of FACTS devices in TEP problem. FACTS devices such as fixed series capacitors (FSCs) are considered in the multistage TEP problem to beter utilize the whole transfer capacity of the network and, consequently, to postpone or reduce the investment in new transmission lines. An excellent benefit-cost ratio can be expected from integration of FSC in multistage transmission expansion planning. The results obtained by using some real test systems indicate that the inclusion of FSCs in the TEP problem is a viable and cost-effective strategy for transmission utilities and national planning bureaus. / Doutor

Protection and Control (P&C) devices requiring accurate timing within a power transmission substation are commonly synchronized by distributed Global Positioning System (GPS) receivers. However, utilities now request a timing system that is less dependent on the direct use of distributed GPS receivers, because of the reliability issue of GPS receivers. In addition, to reduce device-to-device cabling and enable interoperability among devices from multiple vendors, utilities are looking to adopt the Ethernet based IEC 61850 protocol suites to complement or replace a conventional hardwired secondary P&C system. The IEEE 1588-2008 synchronization protocol is a network based time synchronization technique which can co-exist with the IEC 61850 applications and deliver sub-microsecond timing accuracy. A number of IEC 61850 applications require seamless communication redundancy, whilst existing technologies used in a substation only recover communications tens of milliseconds after a communication failure. Alternatively, the newly released IEC 62439-3 Parallel Redundancy Protocol (PRP) and High-availability Seamless Redundancy (HSR) can achieve seamless redundancy by transmitting duplicate data packets simultaneously in various networks and this can satisfy the extremely high reliability requirements of transmission substations. Considering the benefits, a unified network integrating IEEE 1588 and IEC 62439 PRP/HSR can be foreseen in future substations, but utilities need confidence in these technologies before real deployment. Hence, it is necessary to conduct comprehensive tests on such a timing system so that better insight into the performance and limitation can be obtained. This thesis first investigates the feasibility to integrate IEEE 1588 and IEC 62439 PRP into a single Ethernet network using a simulation tool and subsequently presents how the hardware testbed is established. Meanwhile, although GPS receivers are commonly used for time synchronization in the power industry, their performance might not be fully investigated before deployment. Hence, this thesis also proposes a procedure to assess the performance in terms of long term stability and transient behaviour of a timing system merely based on GPS receivers and one based on a mixture of GPS receivers and IEEE 1588 devices. Test results indicate whichever system is used, careful design of equipment, proper installation and appropriate engineering are required to satisfy the stringent accuracy requirements for critical automation applications in power system.

Thesis (Master of Engineering in Electrical Engineering))--Cape Peninsula University of Technology, 2018. / Transformer Differential and overcurrent schemes are traditionally used as main and backup protection respectively. The differential protection relay (SEL487E) has dedicated harmonic restraint function which blocks the relay during the transformer magnetizing inrush conditions. However, the backup overcurrent relay (SEL751A) applied to the transformer protection does not have a harmonic restraint element and trips the overcurrent relay during the inrush conditions. Therefore, to prevent the malfunction caused by the transformer magnetizing inrush current, a novel harmonic blocking method is developed, implemented and tested in the RSCAD simulation environment. The IEEE 14 bus transmission system is considered as a case study. The IEEE 14 bus system is modelled and simulated in the DIgSILENT and RSCAD simulation environments respectively. The developed harmonic blocking scheme is implemented in the Hardware-In-the-Loop (HIL) simulation environment using Real-Time Digital Simulator and numerical protection IEDs. The developed scheme uses the Harmonic Blocking element (87HB) of the transformer differential relay (SEL487E) to send an IEC61850 GOOSE-based harmonic blocking signal to the backup overcurrent relay (SEL751A) to inhibit it from tripping during the transformer magnetizing inrush current conditions. The hardwired and GOOSE simulation results are analysed for the transformer differential protection and the backup overcurrent protection schemes for internal, external events and transformer magnetizing inrush current conditions. The simulation results proved that the IEC61850 standard-based protection scheme is faster than the hardwired. Therefore, the speed and reliability are improved using the IEC61850 standard-based GOOSE applications to the transformer digital protective relaying system.

[pt] Planejar a expansão de sistemas de transmissão de energia elétrica constitui uma tarefa complexa dentro do planejamento do setor elétrico. De acordo com os critérios vigentes, hoje no Brasil, procura-se abordar o problema através de um enfoque de programação matemática. É feito um estudo das técnicas em uso e dos modelos de análise de redes de transmissão. Em seguida é proposta uma nova metodologia para resolver o problema, levando em conta a cultura dos planejadores que podem, assim, interagir com os programas, aperfeiçoando o planejamento. Foi elaborado um modelo de programação inteira, capaz de gerar inúmeras alternativas de planejamento para um dado ano. Estas alternativas são analisadas e concatenadas, obtendo-se o planejamento ao longo do tempo. Apresenta-se um caso real, do planejamento da expansão do sistema sul do Brasil, comparando-se os resultados obtidos com os de outras metodologias. / [en] The plannification of the transmission system expansion is a very complex problem. In this work it is proposed a mathematical programming model to solve it, taking in account the restrictions established by the brazilian electric sector. It is shown the characteristics of some technics for solving the problem and a brief description of the transmission network analysis methods is also presented. It is proposed a new methodology to solve the planning problem, taking in account the planners experience. They are able to interfere on the process interacting with the program looking fot better solutions. An integer programming model was developped to obtain Several distinct expanded configurations for every year of the planning horizon. These configurations are analysed and then linked year, to obtain an expansion policy of the transmission sistem. It is presented the actual planning of the southern brazilian system, and the result obtained by this model are compared with those obtained by other methodologies.

Made available in DSpace on 2015-07-13T12:10:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-02-27. Added 1 bitstream(s) on 2015-07-13T12:25:33Z : No. of bitstreams: 1 000836334.pdf: 1535440 bytes, checksum: 8662c660666cc734fb6a0b7771db7959 (MD5) / Esta dissertação apresenta a modelação, metodologia de projeto e os principais resultados de simulação para um elemento eletromagnético de transmissão indutiva de energia elétrica sem fios, aplicado em postos de abastecimento de Veículos Elétricos (VE) puros. A estrutura proposta é composta por no mínimo dois indutores, sendo um deles o emissor e o outro o receptor de energia. Realizou-se uma revisão bibliográfica das estruturas dos sistemas utilizados para a transmissão de energia eletromagnética sem fios (wireless) e, predominantemente, as mesmas utilizam-se de indutores com formatos espirais cilíndricos ou quadrados, para formar os elementos para transmissão de energia. Neste contexto, este trabalho baseou-se apenas em indutores com formato espiral cilíndrico, sendo estes analisados com base nas teorias do eletromagnetismo, partindo-se da Lei de Biot Savart e da Terceira Lei de Maxwell, com o intuito de obter-se os principais parâmetros de projeto para o elemento de transferência indutiva de potência (IPT - Inductive Power Transfer), quais sejam: Indutância Mútua (emissor/receptor), Indutância Própria (emissor) e Fator de Acoplamento (emissor/receptor). A fim de comprovar a exatidão da metodologia teórica desenvolvida, adotaram-se modelos computacionais utilizando-se o software Comsol ®, onde se construiu o modelo físico do elemento de transmissão de energia (IPT), para cada caso analisado. Os resultados obtidos decorrentes da modelação teórica proposta são inéditos e o trabalho pioneiro em determinar algebricamente um método de cálculo para o acoplamento mútuo entre indutores com geometrias espirais cilíndricas que, quando comparados com os resultados de simulações obtidos através do Comsol ®, demonstraram-se praticamente exatos. Considerando-se a aplicação num estudo de caso de transmissão de energia sem fios (WPT - Wireless Power Transfer), para um Veículo Elétrico (VE) puro em escala... / This work proposes a modeling, design methodology and shows the main simulation results to the development of a Wireless Power Transmission (WPT) element, applied to pure Electric Vehicles (EV). The proposed structure is composed of at least two inductors, composing a transmitter and an energy receiver with weak magnetic coupling among them, considering a far-field energy-transfer method. Considering a literature review for the structures of the systems used for Wireless Power Transmission (WPT), it was observed the use of cylindrical spiral or square shapes, predominantly, in order to compose the inductive elements for power transmission. In this context, this work was based only on inductors with cylindrical spiral shape, which was analyzed based on electromagnetism theories. The proposed methodology starts from the Biot Savart Law and the Third Maxwell Law, in order to obtain the key design parameters for the inductive power transfer element (IPT - Inductive Power Transfer), which are: Mutual Inductance (transmitter / receiver), Self Inductance (transmitter) and Coupling Factor (transmitter / receiver). In order to prove the accuracy of the developed theoretical methodology, was adopted a computational model using the Comsol® software, considering a physical model for the designed IPT element. The results obtained from the proposed theoretical modeling are original and this is a pioneering work in determining algebraically a calculation method for mutual coupling between cylindrical spiral inductors that, when compared with the simulation results obtained by Comsol®, demonstrated practically exact. Furthermore, considering the application in a small-scale case study to WPT, for a pure Electric Vehicle (EV), an important contribution presented in this work is the analysis of arrangements for the inductive element of power transmitter, presenting its advantages and disadvantages and the best configuration for the case study. It should ...

Made available in DSpace on 2014-12-02T11:16:57Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-02-27Bitstream added on 2014-12-02T11:20:50Z : No. of bitstreams: 1 000797343.pdf: 769171 bytes, checksum: e4b6a7c175e5957d6ca52df5c59819d1 (MD5) / Neste trabalho foi apresentado uma nova modelagem matemática para problemas de Planejamento da expansão de sistemas de transmissão ao longo prazo que permite uma mudança no conceito de expansão de sistema de transmissão. Nos problemas de planejamento da expansão de sistemas de transmissão tradicionais apenas as adições de linhas candidatas são consideradas. Neste trabalho um novo conceito de planejamento da expansão do sistema de transmissão é encontrar uma nova solução para a topologia base onde todas as linhas estão temporariamente desconectadas e a implementação dessas linhas são reconsideradas quando elas podem voltar à sua posição anterior. Portanto as linhas da topologia de base não será restabelecida se impedir o desempenho do sistema. Depois um novo problema é resolvido para encontrar o plano futuro da rede do sistema elétrico, com a adição de novas linhas de candidatas na topologia base modificada. A fim de encontrar um plano mais eficiente para a rede futura, a metodologia proposta é implementada usando a linguagem de modelagem para a programação matemática (AMPL) e solucionada usando o solver comercial CPLEX. A fim de validar a abordagem proposta e fazer alguma comparação com o método na literatura, três sistemas de testes são realizados, tais como: o sistema de 24-Bus IEEE teste com 41 linhas de candidatas, um estudos de casos práticos do sistema de 46-Bus do Sul do Brasil com 79 linhas de candidatas, e do sistema colombiano 93-Bus com 155 candidatas. Para sistemas de grande porte, a fim de facilitar a implementação do modelo matemático, uma estratégia é apresentada para reduzir o espaço de busca das barras em que a geração ou a demanda. Nos problemas de planejamento da expansão da transmissão geralmente nos deparamos com um problema de programação não-linear inteira mista (PNLIM) usando o modelo DC, o que torna impossível usar o solver linear ... / In this work and in order to solve the long-term transmission expansion planning problems, a novel mathematical model which is based on a change in the concept of expanding a transmission system is presented. In traditional transmission system expansion planning, only the additions of candidate lines are considered. In this work, a new concept of transmission system expansion planning is to find a new solution for the base topology where all the lines are temporarily disconnected and the implementation of these lines are reconsidered when they may return to their previous position. Therefore, the lines of the base topology will not be reconnected if they prevent the system performance. Afterwards a new problem is solved to find the future plan of the electrical system network with the addition of new candidate lines in the modified base topology. In order to find a more efficient plan for the future network, the proposed methodology is implemented using a Modeling Language for Mathematical Programming (AMPL) and solved using the commercial solver of CPLEX. In order to validate the proposed approach and make some comparison with the method in the literature, three test systems are conducted such as: the 24-Bus IEEE test system with 41 candidate lines, a practical case studies of 46-Bus South Brazilian system with 79 candidate lines, and the 93-Bus Colombian system with 155 candidates. For large-scale systems, in order to facilitate the implementation of the mathematical model, a strategy to reduce the search space of the buses in which the generation or demand has been presented. In the transmission expansion planning problems, usually we face with a mixed integer non-linear programming problem (MINLP) using the DC model, which make it impossible to use the linear solver of CPLEX. The strategy to overcome this problem is using the disjunctive linear model, which is a DC linear equivalent model. The ...

The use of HVDC has many benefits over HVAC for some specific power transmission purposes. However, two major problems with HVDC links are that the converters produce harmonics and consume reactive power. Electrical filters are used to compensate for this and are a major cost driver of HVDC links. An accurate analysis of the modulation makes it possible to design an optimal filter solution in order to make the link financial viable. This report investigates how the complex cross-modulation phenomenon affects the harmonics. The investigation is limited to line-commutated converter technology (LCC) and excludes the newer voltage-source converter technology (VSC) for which the crossmodulation behavior is very different and requires completely different analysis techniques. This report refers to several MATLAB programs. All of these have been developed by the author as part of this thesis work. The report starts by explaining analytically, with the help of switching functions, how harmonics are cross-modulated across line-commutated converters. It is then explained and shown how a MATLAB program, BOWSER, in the time-domain can be used to calculate accurate switching functions when the converter is supplied with a general voltage source and when the DC current contains ripple. After that it is explained and shown how a second MATLAB program, DONKEYKONG, can be created to model an HVDC link in the frequency domain by iterating BOWSER. The cross-modulation phenomena is then finally analyzed in the frequency domain with the help of DONKEYKONG. The result is that the cross-modulation phenomenon can be divided into two groups, affected by grid and DC-side impedance as well as the overlap angle variation. Which will affect the characteristic and non-characteristic harmonics in different ways. It was found that the characteristic harmonics are affected by the cross-modulation due to grid and DC-side impedance by up to 12 % and that low order non-characteristic harmonics can diverge up to 900 % when the converter was supplied with 1 % fundamental unbalance. It also showed that the non-characteristic harmonics have almost the same amplitude for all power transmission levels of the HVDC link. The report shows that the cross-modulation caused by the grid and DC-side impedance, which is sometimes ignored or treated in a simplified way, can affect the practical filter design a lot. It also shows step by step how the MATLAB programs are created

Made available in DSpace on 2014-06-11T19:22:33Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-08-30Bitstream added on 2014-06-13T19:47:48Z : No. of bitstreams: 1 vanderlinde_jb_me_ilha.pdf: 817450 bytes, checksum: f55727575f9ad09191bc30a0419b1f24 (MD5) / A presente pesquisa considera a análise teórica e a implementação computacional do algoritmo Dual Simplex Canalizado especializado na reotimização eficiente dos subproblemas gerados pelo algoritmo Branch and Bound para resolver problemas de Programação Linear Inteiro Misto. Juntamente com estes algoritmos é implementado o algoritmo Primal Simplex Canalizado para resolver o problema de Programação Linear inicial resultante do problema Programação Linear Inteiro Misto após desconsiderar a restrição de integralidade das variáveis. Estes algoritmos, adequadamente analisados e sistematizados são implementados através da linguagem computacional FORTRAN 77 e empregados no Planejamento da Expansão de Sistemas Transmissão modelados através do Modelo de Transportes que resulta em um problema de Programação Linear Inteiro Misto. / This research considers the theoretical analysis and computational implementation of the Dual Simplex algorithmfor Bounded Variables specializes in efficient re-optimization of sub-problems generated by the Branch and Bound algorithm to solve Mixed-Integer Linear Programming problems. Along with these algorithms has been implemented Primal Simplex algorithm for Bounded Variables to solve the initial Linear Programming problem result of a Mixed-Integer Linear Programming problem after relaxing the integrality of the variables. These algorithms has been adequately analyzed and implemented via the computer language FORTRAN 77. The methodology has been tested on the Transmission Network Expansion Planning based on a transportation model that results in a Mixed-Integer Linear Programming.