Localização Ótima de Aparelhos de Corte Normalmente Abertos e Normalmente Fechados em Redes de Distribuição

Tipicamente as redes elétricas de distribuição apresentam uma topologia parcialmente malhada e são exploradas radialmente. A topologia radial é obtida através da abertura das malhas nos locais que otimizam o ponto de operação da rede, através da instalação de aparelhos de corte que operam normalmente abertos. Para além de manterem a topologia radial, estes equipamentos possibilitam também a transferência de cargas entre saídas, aquando da ocorrência de defeitos. As saídas radiais são ainda dotadas de aparelhos de corte que operam normalmente fechados, estes têm como objetivo maximizar a fiabilidade e isolar defeitos, minimizando a área afetada pelos mesmos. Assim, na presente dissertação são desenvolvidos dois algoritmos determinísticos para a localização ótima de aparelhos de corte normalmente abertos e fechados, minimizando a potência ativa de perdas e o custo da energia não distribuída. O algoritmo de localização de aparelhos de corte normalmente abertos visa encontrar a topologia radial ótima que minimiza a potência ativa de perdas. O método é desenvolvido em ambiente Matlab – Tomlab, e é formulado como um problema de programação quadrática inteira mista. A topologia radial ótima é garantida através do cálculo de um trânsito de potências ótimo baseado no modelo DC. A função objetivo é dada pelas perdas por efeito de Joule. Por outro lado o problema é restringido pela primeira lei de Kirchhoff, limites de geração das subestações, limites térmicos dos condutores, trânsito de potência unidirecional e pela condição de radialidade. Os aparelhos de corte normalmente fechados são localizados ao longo das saídas radiais obtidas pelo anterior algoritmo, e permite minimizar o custo da energia não distribuída. No limite é possível localizar um aparelho de corte normalmente fechado em todas as linhas de uma rede de distribuição, sendo esta a solução que minimiza a energia não distribuída. No entanto, tendo em conta que a cada aparelho de corte está associado um investimento, é fundamental encontrar um equilíbrio entre a melhoria de fiabilidade e o investimento. Desta forma, o algoritmo desenvolvido avalia os benefícios obtidos com a instalação de aparelhos de corte normalmente fechados, e retorna o número e a localização dos mesmo que minimiza o custo da energia não distribuída. Os métodos apresentados são testados em duas redes de distribuição reais, exploradas com um nível de tensão de 15 kV e 30 kV, respetivamente. A primeira rede é localizada no distrito do Porto e é caraterizada por uma topologia mista e urbana. A segunda rede é localizada no distrito de Bragança e é caracterizada por uma topologia maioritariamente aérea e rural.

Verfahren zur direkten Implementierung von Algorithmen auf Gatterebene

Bit serial, processing, digital signal processing, transmission, time division, linear programming, linear optimization

Optimal operation of multiproduct batch plants

Multiproduct plants, Dynamic Optimization, Mixed Integer Linear/Non-Linear Programming, Scheduling

General equilibrium with asymmetric information: a dual approach

We study markets where the characteristics or decisions of certain agents are relevant but not known to their trading partners. Assuming exclusive transactions, the environment is described as a continuum economy with indivisible commodities. We characterize incentive efficient allocations as solutions to linear programming problems and appeal to duality theory to demonstrate the generic existence of external effects in these markets. Because under certain conditions such effects may generate non-convexities, randomization emerges as a theoretic possibility. In characterizing market equilibria we show that, consistently with the personalized nature of transactions, prices are generally non-linear in the underlying consumption. On the other hand, external effects may have critical implications for market efficiency. With adverse selection, in fact, cross-subsidization across agents with different private information may be necessary for optimality, and so, the market need not even achieve an incentive efficient allocation. In contrast, for the case of a single commodity, we find that when informational asymmetries arise after the trading period (e.g. moral hazard; ex post hidden types) external effects are fully internalized at a market equilibrium.

Extracción de parámetros de un resonador FBAR por optimización

L’objectiu d’aquest projecte que consisteix a elaborar un algoritme d’optimització que permeti, mitjançant un ajust de dades per mínims quadrats, la extracció dels paràmetres del circuit equivalent que composen el model teòric d’un ressonador FBAR, a partir de les mesures dels paràmetres S. Per a dur a terme aquest treball, es desenvolupa en primer lloc tota la teoria necessària de ressonadors FBAR. Començant pel funcionament i l’estructura, i mostrant especial interès en el modelat d’aquests ressonadors mitjançant els models de Mason, Butterworth Van-Dyke i BVD Modificat. En segon terme, s’estudia la teoria sobre optimització i programació No-Lineal. Un cop s’ha exposat la teoria, es procedeix a la descripció de l’algoritme implementat. Aquest algoritme utilitza una estratègia de múltiples passos que agilitzen l'extracció dels paràmetres del ressonador.

Ordering Policy Rules with an Unconditional Welfare Measure

The unconditional expectation of social welfare is often used to assess alternative macroeconomic policy rules in applied quantitative research. It is shown that it is generally possible to derive a linear - quadratic problem that approximates the exact non-linear problem where the unconditional expectation of the objective is maximised and the steady-state is distorted. Thus, the measure of pol icy performance is a linear combinat ion of second moments of economic variables which is relatively easy to compute numerically, and can be used to rank alternative policy rules. The approach is applied to a simple Calvo-type model under various monetary policy rules.

Devolution dynamics of Spanish local government

Over the last few years, ther has been a devolutionary tendency in many developed and developing countries. In this article we propose a methodology to decompose whether the benefits in terms of effciency derived from transfers of powers from higher to municipal levels of government "the "economic dividend" of devolution) might increase over time. This methodology is based on linear programming approaches for effciency measurement. We provide anapplication to Spanish municipalities, which have had to adapt to both the European Stability and Growth Pact as well as to domestic regulation seeking local governments balanced budget. Results indicate that efficiency gains from enhaced decentralization have increased over time. However, the way through which these gains accrue differs across municipalities -in some cases technical change is the main component, whereas in others catching up dominates.

The Multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria

A multiple-partners assignment game with heterogeneous sales and multiunit demands consists of a set of sellers that own a given number of indivisible units of (potentially many different) goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents' utilities that are attainable at equilibrium.

The achievable region approach to the optimal control of stochastic systems

The achievable region approach seeks solutions to stochastic optimisation problems by: (i) characterising the space of all possible performances(the achievable region) of the system of interest, and (ii) optimisingthe overall system-wide performance objective over this space. This isradically different from conventional formulations based on dynamicprogramming. The approach is explained with reference to a simpletwo-class queueing system. Powerful new methodologies due to the authorsand co-workers are deployed to analyse a general multiclass queueingsystem with parallel servers and then to develop an approach to optimalload distribution across a network of interconnected stations. Finally,the approach is used for the first time to analyse a class of intensitycontrol problems.

Measuring and explaining farm inefficiency in a panel data set of mixed farms

This paper aims to estimate a translog stochastic frontier production function in the analysis of a panel of 150 mixed Catalan farms in the period 1989-1993, in order to attempt to measure and explain variation in technical inefficiency scores with a one-stage approach. The model uses gross value added as the output aggregate measure. Total employment, fixed capital, current assets, specific costs and overhead costs are introduced into the model as inputs. Stochasticfrontier estimates are compared with those obtained using a linear programming method using a two-stage approach. The specification of the translog stochastic frontier model appears as an appropriate representation of the data, technical change was rejected and the technical inefficiency effects were statistically significant. The mean technical efficiency in the period analyzed was estimated to be 64.0%. Farm inefficiency levels were found significantly at 5%level and positively correlated with the number of economic size units.

Looking for orders of magnitude : five essays in trade and the environment and economic geography

General Summary Although the chapters of this thesis address a variety of issues, the principal aim is common: test economic ideas in an international economic context. The intention has been to supply empirical findings using the largest suitable data sets and making use of the most appropriate empirical techniques. This thesis can roughly be divided into two parts: the first one, corresponding to the first two chapters, investigates the link between trade and the environment, the second one, the last three chapters, is related to economic geography issues. Environmental problems are omnipresent in the daily press nowadays and one of the arguments put forward is that globalisation causes severe environmental problems through the reallocation of investments and production to countries with less stringent environmental regulations. A measure of the amplitude of this undesirable effect is provided in the first part. The third and the fourth chapters explore the productivity effects of agglomeration. The computed spillover effects between different sectors indicate how cluster-formation might be productivity enhancing. The last chapter is not about how to better understand the world but how to measure it and it was just a great pleasure to work on it. "The Economist" writes every week about the impressive population and economic growth observed in China and India, and everybody agrees that the world's center of gravity has shifted. But by how much and how fast did it shift? An answer is given in the last part, which proposes a global measure for the location of world production and allows to visualize our results in Google Earth. A short summary of each of the five chapters is provided below. The first chapter, entitled "Unraveling the World-Wide Pollution-Haven Effect" investigates the relative strength of the pollution haven effect (PH, comparative advantage in dirty products due to differences in environmental regulation) and the factor endowment effect (FE, comparative advantage in dirty, capital intensive products due to differences in endowments). We compute the pollution content of imports using the IPPS coefficients (for three pollutants, namely biological oxygen demand, sulphur dioxide and toxic pollution intensity for all manufacturing sectors) provided by the World Bank and use a gravity-type framework to isolate the two above mentioned effects. Our study covers 48 countries that can be classified into 29 Southern and 19 Northern countries and uses the lead content of gasoline as proxy for environmental stringency. For North-South trade we find significant PH and FE effects going in the expected, opposite directions and being of similar magnitude. However, when looking at world trade, the effects become very small because of the high North-North trade share, where we have no a priori expectations about the signs of these effects. Therefore popular fears about the trade effects of differences in environmental regulations might by exaggerated. The second chapter is entitled "Is trade bad for the Environment? Decomposing worldwide SO2 emissions, 1990-2000". First we construct a novel and large database containing reasonable estimates of SO2 emission intensities per unit labor that vary across countries, periods and manufacturing sectors. Then we use these original data (covering 31 developed and 31 developing countries) to decompose the worldwide SO2 emissions into the three well known dynamic effects (scale, technique and composition effect). We find that the positive scale (+9,5%) and the negative technique (-12.5%) effect are the main driving forces of emission changes. Composition effects between countries and sectors are smaller, both negative and of similar magnitude (-3.5% each). Given that trade matters via the composition effects this means that trade reduces total emissions. We next construct, in a first experiment, a hypothetical world where no trade happens, i.e. each country produces its imports at home and does no longer produce its exports. The difference between the actual and this no-trade world allows us (under the omission of price effects) to compute a static first-order trade effect. The latter now increases total world emissions because it allows, on average, dirty countries to specialize in dirty products. However, this effect is smaller (3.5%) in 2000 than in 1990 (10%), in line with the negative dynamic composition effect identified in the previous exercise. We then propose a second experiment, comparing effective emissions with the maximum or minimum possible level of SO2 emissions. These hypothetical levels of emissions are obtained by reallocating labour accordingly across sectors within each country (under the country-employment and the world industry-production constraints). Using linear programming techniques, we show that emissions are reduced by 90% with respect to the worst case, but that they could still be reduced further by another 80% if emissions were to be minimized. The findings from this chapter go together with those from chapter one in the sense that trade-induced composition effect do not seem to be the main source of pollution, at least in the recent past. Going now to the economic geography part of this thesis, the third chapter, entitled "A Dynamic Model with Sectoral Agglomeration Effects" consists of a short note that derives the theoretical model estimated in the fourth chapter. The derivation is directly based on the multi-regional framework by Ciccone (2002) but extends it in order to include sectoral disaggregation and a temporal dimension. This allows us formally to write present productivity as a function of past productivity and other contemporaneous and past control variables. The fourth chapter entitled "Sectoral Agglomeration Effects in a Panel of European Regions" takes the final equation derived in chapter three to the data. We investigate the empirical link between density and labour productivity based on regional data (245 NUTS-2 regions over the period 1980-2003). Using dynamic panel techniques allows us to control for the possible endogeneity of density and for region specific effects. We find a positive long run elasticity of density with respect to labour productivity of about 13%. When using data at the sectoral level it seems that positive cross-sector and negative own-sector externalities are present in manufacturing while financial services display strong positive own-sector effects. The fifth and last chapter entitled "Is the World's Economic Center of Gravity Already in Asia?" computes the world economic, demographic and geographic center of gravity for 1975-2004 and compares them. Based on data for the largest cities in the world and using the physical concept of center of mass, we find that the world's economic center of gravity is still located in Europe, even though there is a clear shift towards Asia. To sum up, this thesis makes three main contributions. First, it provides new estimates of orders of magnitudes for the role of trade in the globalisation and environment debate. Second, it computes reliable and disaggregated elasticities for the effect of density on labour productivity in European regions. Third, it allows us, in a geometrically rigorous way, to track the path of the world's economic center of gravity.

Examination of Highway Maintenance Garages in the U.S. 30 Corridor between Ames and Cedar Rapids, 1988

A linear programming model is used to optimally assign highway segments to highway maintenance garages using existing facilities. The model is also used to determine possible operational savings or losses associated with four alternatives for expanding, closing and/or relocating some of the garages in a study area. The study area contains 16 highway maintenance garages and 139 highway segments. The study recommends alternative No. 3 (close Tama and Blairstown garages and relocate new garage at Jct. U.S. 30 and Iowa 21) at an annual operational savings of approximately $16,250. These operational savings, however, are only the guidelines for decisionmakers and are subject to the required assumptions of the model used and limitations of the study.

Sherali-Adams Relaxations and Indistinguishability in Counting Logics

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional isomorphism. We show that the levels of the Sherali--Adams (SA) hierarchy of linear programming relaxations applied to fractional isomorphism interleave in power with the levels of a well-known color-refinement heuristic for graph isomorphism called the Weisfeiler--Lehman algorithm, or, equivalently, with the levels of indistinguishability in a logic with counting quantifiers and a bounded number of variables. This tight connection has quite striking consequences. For example, it follows immediately from a deep result of Grohe in the context of logics with counting quantifiers that a fixed number of levels of SA suffice to determine isomorphism of planar and minor-free graphs. We also offer applications in both finite model theory and polyhedral combinatorics. First, we show that certain properties of graphs, such as that of having a flow circulation of a prescribed value, are definable in the infinitary logic with counting with a bounded number of variables. Second, we exploit a lower bound construction due to Cai, Fürer, and Immerman in the context of counting logics to give simple explicit instances that show that the SA relaxations of the vertex-cover and cut polytopes do not reach their integer hulls for up to $\Omega(n)$ levels, where $n$ is the number of vertices in the graph.

Predicting diffusion of innovations with self-organisation and machine learning

The main subject of this master's thesis was predicting diffusion of innovations. The prediction was done in a special case: product has been available in some countries, and based on its diffusion in those countries the prediction is done for other countries. The prediction was based on finding similar countries with Self-Organizing Map~(SOM), using parameters of countries. Parameters included various economical and social key figures. SOM was optimised for different products using two different methods: (a) by adding diffusion information of products to the country parameters, and (b) by weighting the country parameters based on their importance for the diffusion of different products. A novel method using Differential Evolution (DE) was developed to solve the latter, highly non-linear optimisation problem. Results were fairly good. The prediction method seems to be on a solid theoretical foundation. The results based on country data were good. Instead, optimisation for different products did not generally offer clear benefit, but in some cases the improvement was clearly noticeable. The weights found for the parameters of the countries with the developed SOM optimisation method were interesting, and most of them could be explained by properties of the products.

Matemática económica con programación lineal

La percepción del joven estudiante de economía es que la práctica con ejercicios es lo único que debe saber. Ésta percepción se puede cambiar con la Programación Lineal ya que unimos teoría y práctica y, al mismo tiempo, mejoramos la capacidad de modelar situaciones económicas y además, hacemos énfasis en el uso de las matemáticas como herramienta eficaz en la mejora de las actividades propias.