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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
101

Transient Seepage in a Variably Saturated Levee: Laboratory Testing, Field Monitoring and Numerical Modeling

Rivera-Hernandez, Xavier Arnaldo 14 December 2018 (has links)
Several hydraulic loadings impose earthen levees to time-dependent variably saturated seepage conditions. The main objective of this study is to improve the analysis of levees under transient seepage with the use of unsaturated soil mechanics. An extensive set of laboratory testing, field monitoring and numerical modeling are performed to analyze a silty sand setback levee located near Seattle, WA. In-situ data obtained from field monitoring are used to monitor suction and effective stress within the levee’s embankment and foundation over the past two years. Soil samples taken from the site are used to perform index, water retention, and unsaturated multi-stage triaxial tests in the laboratory. A finite element model of transient seepage under saturated-unsaturated conditions is then developed and calibrated to reasonably match the field data. The results highlight the need to consider unsaturated soil mechanics along with climatic variables and soil-atmosphere interaction when analyzing levees under transient seepage conditions.
102

Modeling and Parametric Evaluation of a Solar Multistage Flash With Brine Mixing Desalination Plant Using a Novel Dual Tank System

Kaheal, Mohamed M. 11 August 2022 (has links)
No description available.
103

[pt] OTIMIZAÇÃO DE ESTRATÉGIAS DINÂMICAS DE COMERCIALIZAÇÃO DE ENERGIA COM RESTRIÇÕES DE RISCO SOB INCERTEZAS DE CURTO E LONGO PRAZO / [en] RISK-CONSTRAINED OPTIMAL DYNAMIC TRADING STRATEGIES UNDER SHORT- AND LONG-TERM UNCERTAINTIES

ANA SOFIA VIOTTI DAKER ARANHA 23 November 2021 (has links)
[pt] Mudanças recentes em mercados de energia com alta penetração de fontes renováveis destacaram a necessidade de estratégias complexas que, além de maximizar o lucro, proporcionam proteção contra a volatilidade de preços e incerteza na geração. Neste contexto, este trabalho propõe um modelo dinâmico para representar a tomada de decisão sequencial no cenário atual. Ao contrário de trabalhos relatados anteriormente, este método fornece uma estrutura para considerar as incertezas nos níveis estratégico (longo prazo) e operacional (curto prazo) simultaneamente. É utilizado um modelo de programação estocástica multiestágio em que as correlações entre previsões de vazão, geração renovável, preços spot e preços contratuais são consideradas por meio de uma árvore de decisão multi-escala. Além disso, a aversão ao risco do agente comercializador é considerada por meio de restrições intuitivas e consistentes no tempo. É apresentado um estudo de caso do setor elétrico brasileiro, no qual dados reais foram utilizados para definir a estratégia ótima de comercialização de um gerador de energia eólica, condicionada à evolução futura dos preços de mercado. O modelo fornece ao comercializador informações úteis, como o montante contratado ideal, além do momento ótimo de negociação e duração dos contratos. Além disso, o valor desta solução é demonstrado quando comparado a abordagens estáticas, através de uma medida de desempenho baseada no equivalente de certo do problema multiestágio. / [en] Recent market changes in power systems with high renewable energy penetration highlighted the need for complex profit maximization and protection against price volatility and generation uncertainty. This work proposes a dynamic model to represent sequential decision making in this current scenario. Unlike previously reported works, we contemplate uncertainties in both strategic (long-term) and operational (short-term) levels, all considered as pathdependent stochastic processes. The problem is represented as a multistage stochastic programming model in which the correlations between inflow forecasts, renewable generation, spot and contract prices are accounted for by means of interconnected long- and short-term decision trees. Additionally, risk aversion is considered through intuitive time-consistent constraints. A case study of the Brazilian power sector is presented, in which real data was used to define the optimal trading strategy of a wind power generator, conditioned to the future evolution of market prices. The model provides the trader with useful information such as the optimal contractual amount, settlement timing, and term. Furthermore, the value of this solution is demonstrated when compared to state-of-the-art static approaches using a multistage-based certainty equivalent performance measure.
104

Design and Operation of Process Supply Chains under Uncertainty

Patel, Shailesh January 2017 (has links)
This thesis deals with the problems of design and operation of process supply chains. Process supply chains face many challenges due to volatile market conditions, production and transportation delays, and stiff market competition, which ultimately affect their profitability. Supply chain management (SCM) is the process of managing the flow of materials and information within supply chain to optimize the SC performance. SCM is carried out using a hierarchical decision-making framework, where the top most layer looks at network design and the bottom-most layer deals with scheduling day-to-day activities. In this research, the systems engineering principles are applied to devise an improved methodology for supply chain optimization (SCO). First, we consider the design of supply chain in the presence of demand uncertainty. The representation of network topology plays an important role in deriving the optimal network design. In real practice, the shipping cost for transferring goods from one location to another is determined based on service time and quantity. More importantly, the cost associated with establishing a transportation linkage is relatively small for existing transportation infrastructure and can be changed if beneficial. The flexibility of changing the transportation routes is included in the network topology representation by the explicit inclusion of time limited transportation contract agreements. Further, the customer demand is volatile, and it is very difficult to predict accurately. To handle the demand uncertainty, a two-stage stochastic programming formulation is applied in the SC design approach. Next, we consider the problem of handling uncertainty in SC planning by applying a system engineering control principle, robust model predictive control (MPC). The uncertainty in model parameters (yield) and demand are captured by stochastic programming. In this approach, the planning activities are represented by a hybrid model with decisions governed by logical conditions/rulesets. An MPC based rolling horizon control framework is used to schedule the planning activities, where the SC performance is expressed using a multi-criterion objective comprising customer service and economics. The uncertainty in demand and yield are propagated by two mechanisms - an open-loop approach, and an approximate closed-loop strategy. Finally, we consider the problem of integration of SC planning and scheduling. Due to the use of different time scale models for planning and scheduling, the decision derived from the planning layer may result in infeasibility when those targets are implemented at the scheduling level, which ultimately affects the supply chain efficiency. To address this issue, we model tactical and operational planning activities using an integrated hybrid time modeling approach in which the first few planning periods are formulated using an operational planning model and the remaining time periods are modeled with a tactical planning model. The main rationale for formulating an integrated model is that customer demand forecast becomes less accurate for a future time, therefore making a detailed planning model unnecessary. A key benefit of using a hybrid modeling approach is that it avoids the problem of infeasibility encountered in the hierarchical decision framework, as well as the computational burden associated with the use of a detailed planning model over a long time horizon. We employ an MPC based rolling horizon framework as a tactical decision policy where the integrated model is used to predict the system behavior. / Thesis / Doctor of Philosophy (PhD)
105

Statistical Estimation of Software Reliability and Failure-causing Effect

Shu, Gang 02 September 2014 (has links)
No description available.
106

Investigation of experimental and numerical methods, and analysis of stator clocking and instabilities in a high-speed multistage compressor / Investigation des méthodes expérimentales et numériques, et analyse du clocking et des instabilités aérodynamique dans un compresseur axial haute-vitesse multi-étages

Schreiber, Johannes 16 December 2016 (has links)
Les études expérimentales et numériques suivantes visent à la compréhension profonde de l’écoulement se développant dans le compresseur haute-vitesse axial de 3.5 étages CREATE, étudié sur un banc d’essai de 2 MW au Laboratoire de Mécanique des Fluides et Acoustique (LMFA) à Lyon, France. Ce travail a trois objectifs principaux : D’abord, une description globale de l’écoulement avec une identification des limites aux méthodes d’exploration utilisées ; Ensuite, la caractérisation de l’effet du clocking stator-stator dans un compresseur à haute-vitesse ; Troisièmement, l’identification des instabilités à faibles débits pour confirmer les études sur les compresseurs à basse-vitesse et contribuer à plus de compréhension.Il est montré qu’une mauvaise interprétation des données de performance stationnaire se fait facilement en raison des contraintes de mesure et des coefficients de correction sont proposés. À certains endroits dans le compresseur, des limites aux méthodes d’exploration (expérimentales et numériques) de l’écoulement sont identifiées. Cette identification va permettre la poursuite du développement des méthodes. Les principales erreurs de prédiction des simulations concernent la surestimation du blocage induit par l’écoulement de jeu et l’augmentation de pression. En outre, les mesures fournies par les sondes de pression pneumatique surestiment la pression statique en amont des stators. Cette erreur est probablement provoquée par l’interaction entre le champ potentiel du stator et la sonde elle-même. De plus, l’anémométrie Doppler laser surestime la vitesse en aval des stators. Le transport des sillages du rotor à travers des stators n’est pas correctement capturé avec les particules d’ensemencement.Le clocking a seulement un petit effet global dans la bande d’incertitude de mesure dans ce compresseur. Plusieurs contributions à ce faible effet de clocking sont identifiées par l’analyse du transport des structures d’écoulement : Le mélange circonférentiel du sillage de stator et la déformation des sillages le long de leur trajet dans l’écoulement. L’effet local du clocking dépend de la hauteur de veine en raison de la variation de la forme des aubages et du transport des sillages. Des effets positifs et négatifs sont présentés, qui globalement se compensent dans ce compresseur. Les instabilités dans ce compresseur dépendent du point de fonctionnement et des méthodes d’exploration de l’écoulement. Aux points de fonctionnement stables et à la vitesse nominale du compresseur, les résultats numériques montrent une perturbation tournante dans les rotors 2 et 3, alors que les mesures montrent une perturbation tournante que dans le premier rotor et seulement à basse vitesse du compresseur. Dans les deux cas, les perturbations montrent des caractéristiques semblables. Une étude numérique permet d’exclure l’influence des interactions rotor-stator sur la perturbation tournante et met en évidence sa source. Des nouvelles connaissances sur le comportement stable et la périodicité du rotating instability (mesuré) sont dérivées contrairement au comportement instable suggéré par la dénomination et la littérature. Il est montré que cette perturbation évolue en cellule de décrochage tournante à l’approche de la limite de stabilité. A la vitesse nominale du compresseur, une entrée en instabilités de type spike est identifiée expérimentalement. Une description précise de l’apparition brutale du spike et sa différence par rapport à une cellule de décollement tournant sont présentées. / The following experimental and numerical investigations aim at the deep understanding of the flow field in the 3.5 stages high-speed axial compressor CREATE, studied on a 2 MW test rig at the Laboratory of Fluid Mechanics and Acoustics (LMFA) in Lyon, France. This work focuses on three major objectives: Firstly, a global description of the flow field with an identification of limitations to the used exploration methods; Secondly, the characterization of the effect of stator-stator clocking in a high-speed compressor; Thirdly, the identification of instabilities arising at low mass flow rates for confirming studies on low-speed compressors and giving new insights.This work demonstrates that a mis-interpretation of steady performance data occurs easily due to measurement constraints and correction coefficients are proposed. At certain locations in the compressor, the flow field exploration (experimental and numerical) methods are identified to be challenged. This identification will initiate further development of the methods. The main mis-predictions of the simulations concern the over-prediction of the blockage induced by the tip leakage flow and eventually an over-predicted pressure rise. Furthermore, the measurements provided by the pneumatic pressure probes over-estimate the static pressure upstream of the stators. This error is induced by the interaction between the stator potential field and the probe it-self. In addition, the laser Doppler anemometry method over-estimates the velocity downstream the stators. The transport of the rotor wakes through the stators might not be correctly captured with the seeding particles in this high-speed compressor.The investigation of the stator clocking reveals only a small global effect within the measurement uncertainty band. Several contributions to the weak effect of clocking are identified by analysis of the flow structure transport, namely the time-mean mixing out of the stator wakes and the deformation of wakes along their flow path. The local effect of clocking depends on the span-height because of the variation of the circumferential position of the stator wakes and the stator blade shape over the span-height. Local possible positive and negative effects of clocking are identified and are shown to be almost in balance in this compressor. Furthermore, this work demonstrates that the unsteadiness in the flow field is not linked conclusively to the stator clocking.In this compressor, the arising instabilities depend on the operating point and flow field exploration methods. At stable operating points and nominal compressor speed, the numerical results reveal a rotating disturbance in the rotors 2 and 3, whereas the measurements show a rotating disturbance only in the first rotor and only at part speed. In both cases the disturbance exhibits rotating instability like characteristics. An exhaustive numerical study allows to exclude the commonly assumed influence of rotor-stator interactions on the rotating disturbance and pinpoints its source. New insights into the stable behavior and periodicity of the measured rotating instability are derived contrary to the unstable behavior suggested by the naming and literature. This disturbance is shown to evolve into rotating stall cells when approaching the stability limit. At nominal compressor speed, a spike type surge inception is identified I n the measured field. A precise description of the abrupt onset of the spike cell and its difference to a rotating stall cell are presented.
107

O problema integrado de dimensionamento e sequenciamento de lotes no processo de fabricação da cerveja: modelos e métodos de solução / The integrated lot sizing and scheduling problem in the brewing process: models and solution methods

Baldo, Tamara Angélica 19 August 2014 (has links)
Este trabalho aborda o problema multiestágio de planejamento e programação da produção em indústrias cervejeiras. O processo de fabricação de cerveja pode ser dividido em duas etapas principais: preparação do líquido e envase. A primeira etapa ocorre, na maior parte do tempo, dentro de tanques de fermentação e maturação. A segunda ocorre nas linhas de envase, podendo ter início assim que o líquido estiver pronto nos tanques. O tempo de preparação do líquido demora vários dias, enquanto que na maioria das indústrias de bebidas carbonatadas este tempo é de no máximo algumas horas. O objetivo deste estudo é obter planos de produção viáveis que visam otimizar as decisões de programação envolvidas nestes processos. Visitas a cervejarias no Brasil e em Portugal foram realizadas para uma maior familiaridade do processo de produção e dados foram coletados. Modelos de programação inteira mista para representar o problema foram desenvolvidos, baseados em abordagens CSLP (The Continuous Setup Lot-Sizing Problem), GLSP (General Lot Sizing and Scheduling Problem), SPL (Simple Plant Location Problem) e ATSP (Asymmetric Travelling Salesman Problem). Os resultados mostram que os modelos são coerentes e representam adequadamente o problema, entretanto, mostram-se difíceis de serem resolvidos na otimalidade. Esta dificuldade de resolução dos modelos motivou o desenvolvimento de procedimentos MIP-heurísticos, como também de uma metaheurística GRASP (Greedy Randomized Adaptive Search Procedure). As soluções obtidas pelos procedimentos heurísticos são de boa qualidade, quando comparadas ao melhor limitante inferior encontrado por meio da resolução dos modelos matemáticos. Os testes computacionais foram realizados utilizando instâncias geradas com base em dados reais. / This study deals with the multistage lot-sizing and scheduling problem in breweries. The brewing process can be divided into two main stages: preparation and filling of the liquid. The first stage occurs most of the time in fermentation and maturation tanks. The second stage occurs in the filling lines and it can start as soon as the liquid gets ready. The preparation time of the liquid takes several days, while in the carbonated beverage industries this time is at most a few hours. The purpose of this study is to obtain feasible production plans aimed at optimizing the decisions involved in these processes. Visits to brewery industries in Brazil and Portugal were held to a greater familiarity of the production process and data were collected. Mixed integer programming models have been developed to represent the problem, based on approaches for the CSLP (The Continuous Setup Lot-Sizing Problem), GLSP (General Lot Sizing and Scheduling Problem), SPL (Simple Plant Location Problem) and ATSP (Asymmetric Travelling Salesman Problem). The results show that the models are consistent and adequately represent the problem; however, they are difficult to be solved at optimality. This motivated the development of MIP-heuristic procedures, as well as a meta-heuristic GRASP (Greedy Randomized Adaptive Search Procedure). The obtained solutions by the heuristics are of good quality, when compared to the best lower bound found by solving the mathematical models. The tests were conducted using generated instances based on real data.
108

資產配置之動態規劃 / An Application of Dynamic Asset Allocation: Two-period Investigation

蔡秉寰, Tsai, Ping-Huan Unknown Date (has links)
資產配置乃是將資金分散投資到主要的資產類別中,諸如股票、債券、現金等。傳統的均數/變異數方法在資產配置上早已被廣泛的運用。但是,現今的金融情勢多變,多期配置的需求提高,傳統均數/變異數方法只處理單一期間的資產配置,且反應未來的能力不佳,顯然已經不適用。 本論文提供一種多期動態的資產配置,可以改良過去單點估計值的缺點,同時能夠將未來情境納入考量,使多期資產配置更富策略性。並實證在兩期的情況下,期中調整資產組合與不調整的差異性。從而瞭解持續的動態規劃,方能提升資產配置的效率性。 / Asset allocation is the process of dividing an investment fund among major asset classes such as equities, bonds, cash, etc. Traditional mean-variance portfolio selection is widely used for asset allocation. However, as time goes by, the financial condition changes rapidly. The method of mean-variance analysis has some limitations. It not only can’t deal with multiperiod asset allocation, but also cannot reflect future economic circumstances, especially for long-term investments. This research tries to use the method of multi-stage dynamic programming for asset allocation. This method can improve the pits of single estimate in using mean-variance analysis, and take future scenarios into account so that the model will become more useful in practice. The two-period empirical results have shown that using continuous dynamic programming to build strategic asset allocation decision can improve the efficiency of asset allocation.
109

Identitet, kropp og hverdagsliv i et folkelig perspektiv : og erfaringskunnskapens plass innen folkehelsetenkningen / Identity, Body and Everyday Life in a Popularly Perspective : and the Role of Experiential Knowledge within Public Health Thinking

Solheim, Inger Helen January 2013 (has links)
Over the last decades the weight has increased in the Norwegian population. Report no 16 to the Storting, “Prescription for a healthier Norway”, expresses concern for this development and defines important areas of commitment to prevent a further increase in health problems like diabetes 2 and other lifestyle related diseases. The foci described above are all justified by figures and statistical surveys. The dominant approach towards lifestyle related diseases is closely connected with Western medicine. The main tendency in the recommendations is primarily presenting overweight and obesity as something negative and problematic.  This study focuses on self-assessment and self-perception of people that are overweight as well as those of normal weight. The aim is to reveal the collective understanding in a local community that struggles to avoid a further weight-gain in its population. This thesis seeks to, shed light on how the weight- evolvement in the Norwegian society influence peoples individual self-image and body perception. A local community in Norway (“Libygda”) defined by media, some years ago, as the most overweight local community in the country, constitutes the basis for this thesis. Methods like fieldwork, multistage focus group interviews and individual interviews (all carried out in “Libygda”) were used. The main focus in all the approaches is the bottom up strategy gained through the research approach Co-operative Inquiry which implies that both researcher and participants together search to gain insight and new experiential knowledge. In this case about individual health perception, body and identity. The data material is analyzed mainly through Life Mode-Theory, and theories of social capital (and other theories from the Social Science field). Methodological and theoretical approaches within Public Health Work are mainly based in Health Science, whereas this thesis has Social Science (Sociology and Social Anthropology) as its point of departure. The thesis will by its perspective aim to complement the traditional Health Science and offer a supplemental approach to the Science of Public Health. This thesis describes how experience-based perspectives on health and body exist side by side with the medical and Public Health Science perspective. This implies that there exists a parallel understanding of reality, which is rarely focused on by health professionals. If Public Health Work should gain a greater impact on peoples’ everyday life, these experience based and folk perspectives must be taken into consideration and accepted by professionals as relevant. / De siste tiårene har vekten økt i den norske befolkningen. Stortingsmelding nr 16 ”Resept for et sunnere Norge” uttrykker uro for denne utviklingen og definerer viktige satsningsområder for å hindre en økning i antallet diabetes 2 og andre livsstilsrelaterte sykdommer. Satsningsområdene beskrevet over er alle basert på og dokumentert ved statistiske undersøkelser. Hovedtendensen i anbefalingene har som utgangspunkt at overvekt og fedme er assosiert med noe negativt og problematisk. Denne avhandlingens fokus er den subjektive selvoppfatningen til både normalvektige og overvektige. Hensikten er å avdekke den kollektive forståelsen av helse og et godt liv i et lokalsamfunn med overvektsutfordringer i befolkningen. Avhandlingen søker å belyse hvordan vektøkning i det norske samfunnet påvirker individers selvbilde og kroppsforståelse, og hvordan dette speiles på lokalsamfunnsnivå. Et lokalsamfunn i Sør-Norge (”Libygda”), definert av media rundt tusenårsskiftet som den mest overvektige kommunen i Norge, danner utgangspunktet for denne studien. Metoder som feltarbeid, deltagende observasjon, flerstegs fokusgruppeintervju, individuelle intervjuer (alt uført i ”Libygda”) blir benyttet. Hovedfokuset i de metodiske tilnærmingene er en nedenfra-og-opp inngang inspirert av handlingsorientert forskningssamarbeid, hvor både forsker og deltakere sammen søker ny innsikt og erfaringskunnskap om individuell og kollektiv helseoppfatning, kroppsforståelse og identitet. Datamaterialet blir analysert i lys av livsformteori, sosial kapital og andre relevante samfunnsvitenskapelige teorier. Metodiske og teoretiske tilnærminger innen folkehelsearbeidet er ofte knyttet til helseforskningen, mens denne avhandlingen har et samfunnsvitenskapelig (sosiologi og sosialantropologi) utgangspunkt. Avhandlingens perspektiv søker å komplementere tradisjonell helseforskning med en erfaringsbasert tilnærming til folkehelsevitenskapen. Avhandlingen beskriver hvordan erfaringsbaserte og folkelige perspektiver på helse og kropp lever side om side med den medisinske og folkehelsevitenskaplige. Dette innebærer at det eksisterer en parallell forståelse av virkeligheten, som sjelden blir tillagt vekt eller fokusert av helsepersonell eller akademia. Hvis folkehelsearbeid skal få større innflytelse og gjennomslagskraft i menneskers hverdagsliv, må disse erfaringsbaserte og folkelige perspektivene inkluderes av fagfolk.
110

Risk neutral and risk averse approaches to multistage stochastic programming with applications to hydrothermal operation planning problems

Tekaya, Wajdi 14 March 2013 (has links)
The main objective of this thesis is to investigate risk neutral and risk averse approaches to multistage stochastic programming with applications to hydrothermal operation planning problems. The purpose of hydrothermal system operation planning is to define an operation strategy which, for each stage of the planning period, given the system state at the beginning of the stage, produces generation targets for each plant. This problem can be formulated as a large scale multistage stochastic linear programming problem. The energy rationing that took place in Brazil in the period 2001/2002 raised the question of whether a policy that is based on a criterion of minimizing the expected cost (i.e. risk neutral approach) is a valid one when it comes to meet the day-to-day supply requirements and taking into account severe weather conditions that may occur. The risk averse methodology provides a suitable framework to remedy these deficiencies. This thesis attempts to provide a better understanding of the risk averse methodology from the practice perspective and suggests further possible alternatives using robust optimization techniques. The questions investigated and the contributions of this thesis are as follows. First, we suggest a multiplicative autoregressive time series model for the energy inflows that can be embedded into the optimization problem that we investigate. Then, computational aspects related to the stochastic dual dynamic programming (SDDP) algorithm are discussed. We investigate the stopping criteria of the algorithm and provide a framework for assessing the quality of the policy. The SDDP method works reasonably well when the number of state variables is relatively small while the number of stages can be large. However, as the number of state variables increases the convergence of the SDDP algorithm can become very slow. Afterwards, performance improvement techniques of the algorithm are discussed. We suggest a subroutine to eliminate the redundant cutting planes in the future cost functions description which allows a considerable speed up factor. Also, a design using high performance computing techniques is discussed. Moreover, an analysis of the obtained policy is outlined with focus on specific aspects of the long term operation planning problem. In the risk neutral framework, extreme events can occur and might cause considerable social costs. These costs can translate into blackouts or forced rationing similarly to what happened in 2001/2002 crisis. Finally, issues related to variability of the SAA problems and sensitivity to initial conditions are studied. No significant variability of the SAA problems is observed. Second, we analyze the risk averse approach and its application to the hydrothermal operation planning problem. A review of the methodology is suggested and a generic description of the SDDP method for coherent risk measures is presented. A detailed study of the risk averse policy is outlined for the hydrothermal operation planning problem using different risk measures. The adaptive risk averse approach is discussed under two different perspectives: one through the mean-$avr$ and the other through the mean-upper-semideviation risk measures. Computational aspects for the hydrothermal system operation planning problem of the Brazilian interconnected power system are discussed and the contributions of the risk averse methodology when compared to the risk neutral approach are presented. We have seen that the risk averse approach ensures a reduction in the high quantile values of the individual stage costs. This protection comes with an increase of the average policy value - the price of risk aversion. Furthermore, both of the risk averse approaches come with practically no extra computational effort and, similarly to the risk neutral method, there was no significant variability of the SAA problems. Finally, a methodology that combines robust and stochastic programming approaches is investigated. In many situations, such as the operation planning problem, the involved uncertain parameters can be naturally divided into two groups, for one group the robust approach makes sense while for the other the stochastic programming approach is more appropriate. The basic ideas are discussed in the multistage setting and a formulation with the corresponding dynamic programming equations is presented. A variant of the SDDP algorithm for solving this class of problems is suggested. The contributions of this methodology are illustrated with computational experiments of the hydrothermal operation planning problem and a comparison with the risk neutral and risk averse approaches is presented. The worst-case-expectation approach constructs a policy that is less sensitive to unexpected demand increase with a reasonable loss on average when compared to the risk neutral method. Also, we comp are the suggested method with a risk averse approach based on coherent risk measures. On the one hand, the idea behind the risk averse method is to allow a trade off between loss on average and immunity against unexpected extreme scenarios. On the other hand, the worst-case-expectation approach consists in a trade off between a loss on average and immunity against unanticipated demand increase. In some sense, there is a certain equivalence between the policies constructed using each of these methods.

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