This research deals with the optimization of metrology and calibration problems. The optimization involved here is the application scientifically sound operations research techniques to help in solving the problem intended optimally or semi-optimally with a practical time frame. The research starts by exploring the subject of measurement science known as metrology. This involves defining all the constituents of metrology facilities along with their various components. The definitions include the SI units’ history and structure as well as their characteristics. After that, a comprehensive description of most of the operations and parameters encountered in metrology is presented. This involves all sources of uncertainties in most of the parameters that affect the measurements. From the background presented and using all the information within it; an identification of the most important and critical general problems is attempted. In this treatment a number of potential optimization problems are identified along with their description, problem statement definition, impact on the system and possible treatment method. After that, a detailed treatment of the scheduling problem, the calibration interval determination problem and the average outgoing quality problem is presented. The scheduling problem is formulated and modelled as a mixed integer program then solved using LINGO program. A heuristic algorithm is then developed to solve the problem near optimally but in much quicker time, and solution is packaged in a computer program. The calibration interval problem treatment deals with the determination of the optimal CI. Four methods are developed to deal with different cases. The cases considered are the reliability target case, the CI with call cost and failure cost of both first failure and all failures and the case of large number of similar TMDEs. The average out going quality (AOQ) treatment involves the development two methods to assess the AOQ of a calibration facility that uses a certain multistage inspection policy. The two methods are mathematically derived and verified using a simulation model that compares them with an actual failure rate of a virtual calibration facility.

The focus of this thesis is to explore a new mechanism to give added incentive to invest in new capacities in deregulated electricity markets. There is a lot of concern in energy markets, regarding lack of sufficient private sector investment in new capacities to generate electricity. Although some markets are using mechanisms to reward these investments directly, e.g., by governmental subsidies for renewable sources such as wind or solar, there is not much theory to guide the process of setting the reward levels. The proposed mechanism involves a long term planning model, maximizing the social welfare measured as consumers’ plus producers’ surplus, by choosing new generation capacities which, along with still existing capacities, can meet demand. Much previous research in electricity capacity planning has also solved optimization models, usually with continuous variables only, in linear or non-linear programs. However, these approaches can be misleading when capacity additions must either be zero or a large size, e.g., the building of a nuclear reactor or a large wind farm. Therefore, this research includes binary variables for the building of large new facilities in the optimization problem, i.e. the model becomes a mixed integer linear or nonlinear program. It is well known that, when binary variables are included in such a model, the resulting commodity prices may give insufficient incentive for private investment in the optimal new capacities. The new mechanism is intended to overcome this difficulty with a capacity price in addition to the commodity price: an auxiliary mathematical program calculates the minimum capacity price that is necessary to ensure that all firms investing in new capacities are satisfied with their profit levels. In order to test the applicability of this approach, the result of the suggested model is compared with the Ontario Integrated Power System Plan (IPSP), which recommends new generation capacities, based on historical data and costs of different sources of electricity generation for the next 20 years given a fixed forecast of demand.

The focus of this thesis is to explore a new mechanism to give added incentive to invest in new capacities in deregulated electricity markets. There is a lot of concern in energy markets, regarding lack of sufficient private sector investment in new capacities to generate electricity. Although some markets are using mechanisms to reward these investments directly, e.g., by governmental subsidies for renewable sources such as wind or solar, there is not much theory to guide the process of setting the reward levels. The proposed mechanism involves a long term planning model, maximizing the social welfare measured as consumers’ plus producers’ surplus, by choosing new generation capacities which, along with still existing capacities, can meet demand. Much previous research in electricity capacity planning has also solved optimization models, usually with continuous variables only, in linear or non-linear programs. However, these approaches can be misleading when capacity additions must either be zero or a large size, e.g., the building of a nuclear reactor or a large wind farm. Therefore, this research includes binary variables for the building of large new facilities in the optimization problem, i.e. the model becomes a mixed integer linear or nonlinear program. It is well known that, when binary variables are included in such a model, the resulting commodity prices may give insufficient incentive for private investment in the optimal new capacities. The new mechanism is intended to overcome this difficulty with a capacity price in addition to the commodity price: an auxiliary mathematical program calculates the minimum capacity price that is necessary to ensure that all firms investing in new capacities are satisfied with their profit levels. In order to test the applicability of this approach, the result of the suggested model is compared with the Ontario Integrated Power System Plan (IPSP), which recommends new generation capacities, based on historical data and costs of different sources of electricity generation for the next 20 years given a fixed forecast of demand.

The two-dimension packing problem is concerned with the arrangement of items without overlaps inside a container. In particular we have considered the case when the items are circular objects, some of the general examples that can be found in the industry are related with packing, storing and transportation of circular objects. Although there are several approaches we want to investigate the use of formulation space search. Formulation space search is a fairly recent method that provides an easy way to escape from local optima for non-linear problems allowing to achieve better results. Despite the fact that it has been implemented to solve the packing problem with identical circles, we present an improved implementation of the formulation space search that gives better results for the case of identical and non-identical circles, also considering that they are packed inside different shaped containers, for which we provide the needed modifications for an appropriate implementation. The containers considered are: the unit circle, the unit square, two rectangles with different dimension (length 5, width 1 and length 10 width 1), a right-isosceles triangle, a semicircle and a right-circular quadrant. Results from the tests conducted shown several improvements over the best previously known for the case of identical circles inside three different containers: a right-isosceles triangle, a semicircle and a circular quadrant. In order to extend the scope of the formulation space search approach we used it to solve mixed-integer non-linear problems, in particular those with zero-one variables. Our findings suggest that our implementation provides a competitive way to solve these kind of problems.

abstract: The electric transmission grid is conventionally treated as a fixed asset and is operated around a single topology. Though several instances of switching transmission lines for corrective mechaism, congestion management, and minimization of losses can be found in literature, the idea of co-optimizing transmission with generation dispatch has not been widely investigated. Network topology optimization exploits the redundancies that are an integral part of the network to allow for improvement in dispatch efficiency. Although, the concept of a dispatchable network initially appears counterintuitive questioning the wisdom of switching transmission lines on a more regu-lar basis, results obtained in the previous research on transmission switching with a Direct Current Optimal Power Flow (DCOPF) show significant cost reductions. This thesis on network topology optimization with ACOPF emphasizes the need for additional research in this area. It examines the performance of network topology optimization in an Alternating Current (AC) setting and its impact on various parameters like active power loss and voltages that are ignored in the DC setting. An ACOPF model, with binary variables representing the status of transmission lines incorporated into the formulation, is written in AMPL, a mathematical programming language and this optimization problem is solved using the solver KNITRO. ACOPF is a non-convex, nonlinear optimization problem, making it a very hard problem to solve. The introduction of bi-nary variables makes ACOPF a mixed integer nonlinear programming problem, further increasing the complexity of the optimization problem. An iterative method of opening each transmission line individually before choosing the best solution has been proposed as a purely investigative approach to studying the impact of transmission switching with ACOPF. Economic savings of up to 6% achieved using this approach indicate the potential of this concept. In addition, a heuristic has been proposed to improve the computational efficiency of network topology optimization. This research also makes a comparative analysis between transmission switching in a DC setting and switching in an AC setting. Results presented in this thesis indicate significant economic savings achieved by controlled topology optimization, thereby reconfirming the need for further examination of this idea. / Dissertation/Thesis / M.S. Electrical Engineering 2011

Energy systems with a high portion of renewable energy from wind and solar power can suffer from fluctuations in production due to weak winds or cloudy weather, which may affect the electricity price. When producing heat and power in a combined heat and power plant, an additional heat storage tank can be used to store the heat surplus which is obtained when the power production is high, and the heat demand is low. To optimize heat and power production economically, short-term planning can be applied. Short-term planning covers the production in the near future of 1-3 days. The optimization in this degree project is based on the district heating production, which means that the heating demand always needs to be fulfilled. The district heating production is based on the weather. Therefore a suitable period for simulation is three days due to the accuracy of the weather forecasts are reasonable. The optimization is performed on the district heat system in Gävle, Sweden. The system comprises several different production units, such as combined heat and power plants, backup plants, and industrial waste heat recovery. Two different models are made, one using linear programming and one using mixed integer non-linear programming. The model stated as a linear programming problem is not as accurate as of the one stated as a mixed integer non-linear programming problem which uses binary variables. Historical input data from Bomhus Energi AB, a company owned together by the local heat and power supplier Gävle Energi AB and the pulp and paper manufacturer BillerudKorsnäs AB, was given to simulate different scenarios. The different scenarios have various average temperatures and in some scenarios are there some issues with the pulp and paper industry affecting the waste heat recovery. In all scenarios is the heat storage tank charged when the demand is low and then discharged when the demand increases to avoid starting some of the more expensive backup plants if possible. The simulation time varies a lot between the two approaches, from a couple of seconds to several hours. Particularly when observing scenarios with a rather high demand since the backup generators use binary variables which take a lot of time to solve.

In this research, the focus is on improving a designer's capability to determine near-optimal sizes of components for a given system architecture. Component sizing is a hard problem to solve because of the presence of competing objectives, requirements from multiple disciplines, and the need for finding a solution quickly for the architecture being considered. In current approaches, designers rely on heuristics and iterate over the multiple objectives and requirements until a satisfactory solution is found. To improve on this state of practice, this research introduces advances in the following two areas: a.) Formulating a component sizing problem in a manner that is convenient to designers and b.) Solving the component sizing problem in an efficient manner so that all of the imposed requirements are satisfied simultaneously and the solution obtained is mathematically optimal. In particular, an acausal, algebraic, equation-based, declarative modeling approach is taken to solve component sizing problems efficiently. This is because global optimization algorithms exist for algebraic models and the computation time is considerably less as compared to the optimization of dynamic simulations. In this thesis, the mathematical programming language known as GAMS (General Algebraic Modeling System) and its associated global optimization solvers are used to solve component sizing problems efficiently. Mathematical programming languages such as GAMS are not convenient for formulating component sizing problems and therefore the Systems Modeling Language developed by the Object Management Group (OMG SysML ) is used to formally capture and organize models related to component sizing into libraries that can be reused to compose new models quickly by connecting them together. Model-transformations are then used to generate low-level mathematical programming models in GAMS that can be solved using commercial off-the-shelf solvers such as BARON (Branch and Reduce Optimization Navigator) to determine the component sizes that satisfy the requirements and objectives imposed on the system. This framework is illustrated by applying it to an example application for sizing a hydraulic log splitter.

The objective of this project is to develop an operational scheduling model for Sasol Mining’s coal handling facility, Sasol Coal Supply (referred to as SCS), to optimise daily operations. In this document, the specific scheduling problem at SCS is presented and solved using Mixed Integer Non-Linear Programming (MINLP) continuous time representation techniques. The most recent MINLP scheduling techniques are presented and applied to an example problem. The assumption is made that the results from the example problem will display trends which will apply to the SCS scheduling problem as well. Based on this assumption, the unit-specific event based continuous time formulation is chosen to apply to the SCS scheduling problem. The detail mathematical formulation of the SCS scheduling problem, based on the chosen technique, is discussed and the necessary changes presented to customise the formulation for the SCS situation. The results presented show that the first phase model does not solve within 72 hours. A solution time of more than three days is not acceptable for an operational scheduling model in a dynamic system like SCS. Various improvement approaches are applied during the second phase of the model development. Special Ordered Sets of Type 1 (SOS1) variables are successfully applied in the model to reduce the amount of binary variables. The time and duration constraints are restructured to simplify the structure of the model. A specific linearization and solution technique is applied to the non-linear equations to ensure reduced model solution times and reliable results. The improved model for one period solves to optimality within two minutes. This dramatic improvement ensures that the model will be used operationally at SCS to optimise daily operations. The scheduling model is currently being implemented at SCS. Examples of the input variables and output results are presented. It is concluded that the unit-specific event based MINLP continuous time formulation method, as presented in the literature, is not robust enough to be applied to an operational industrial-sized scheduling problem such as the SCS problem. Customised modifications to the formulation are necessary to ensure that the model solves in a time acceptable for operational use. However, it is proved that Mixed Integer Non-linear Programming (MINLP) can successfully be applied to optimise the scheduling of an industrial-sized plant such as SCS. Although more research is required to derive robust formulation techniques, the principle of using mathematical methods to optimise operational scheduling in industry can dramatically impact the way plants are operated. The optimisation of daily schedules at SCS by applying the MINLP continuous time scheduling technique, has made a significant contribution to the coal handling industry. Finally, it can be concluded that the SCS scheduling problem was successfully modelled and the operational scheduling model will add significant value to the Sasol Group. / Dissertation (MEng (Industrial Engineering))--University of Pretoria, 2006. / Industrial and Systems Engineering / unrestricted

L’objectif de ces travaux est de développer une méthode d’aide à la conception des réseaux de chaleur urbains (RCU). Cette méthode utilise un modèle de type MINLP (Mixed Integer Non Linear Programming) pour l’optimisation simultanée de la configuration et du dimensionnement d’un RCU. Aux variables continues pour l’aide au dimensionnement (température, vitesse, diamètre, aire des échangeurs), s’ajoutent des variables binaires aidant à définir la configuration du réseau (maillage et choix des technologies). La fonction objectif à minimiser est le coût total (capex et opex), qui est soumise à un ensemble de contraintes non linéaires (p. ex. pertes thermiques et de charge, bilans). La méthode développée dans ce manuscrit offre la possibilité de connecter en cascade des consommateurs n’ayant pas les mêmes besoins en température, et de réaliser des réseaux bouclés (une canalisation par tranchée). Elle permet aussi de choisir : les consommateurs à connecter au RCU, le ou les sites de production ainsi que le type de technologie utilisée. Enfin la bonne prise en compte de la physique permet de choisir le meilleur compromis entre pertes thermiques et pertes de charge, sur une large gamme de température. Cette formulation permet donc d’optimiser des réseaux de 4éme génération et de démontrer la rentabilité de l’intégration d’EnR&R sur le long terme (30 ans). Un premier travail est réalisé afin de proposer une méthodologie de résolution en plusieurs étapes permettant l’obtention de l’optimum global. Différents cas d’études académiques sont utilisés pour présenter les intérêts multiples de cette formulation. Enfin la comparaison avec un réseau existant a permis de démontrer la cohérence des résultats du modèle et a servi de base pour l’optimisation d’un cas d’étude de grande dimension. Plusieurs études de sensibilité post-optimale sont réalisées afin de démontrer l’intérêt de cet outil pour l’aide à la conception initiale ou l’extension de RCU existants. / The aim of this thesis is to develop a method that provides design assistance for District Heating Network (DHN). This tool allows simultaneously the optimization of the configuration and its sizing, thanks to an MINLP formulation (Mixed Integer Non-Linear Programming). Binary variables help to choose the optimal configuration (network layout and technologies of production), whereas continuous variables help DHN sizing (temperature, diameter, velocity, heat exchanger area, thermal generating capacity …). The objective function to minimize is the total cost (capex and opex), subjected to numerous nonlinear constraints (e.g. thermal losses, pressure drop, energy balance).This method enables to design temperature cascade between consumers, when consumer temperature requirements are different, and also looped network (only one pipe in one trench). It helps also the decision to connect (or not) consumers to the main network and also the location(s) and type(s) of the heating plant. Moreover, the arbitrage between heat losses and pressure drops is taken into account thanks to physical considerations (non-linear equations). Eventually, it is possible to design 4th generation DHN and prove their financial profitability over the long terms (30 years). First a multi-step resolution strategy is proposed to ensure finding global optimum of the complex MINLP problem. Then academic study cases are analyzed to underline the numerous assets of the formulation. Finally, the optimal design compared to an existing DHN ensures the consistency of the method and allows to build a study case at a wider scale, which can be solved thanks to the comprehensive strategy developed. The design assistance method is available for initial design as well as for extension of existing DHN.