Column-generation and interior point methods applied to the long-term electric power-planning problem

Aquesta tesi s'adreça al problema de planificació de la generació elèctrica a llarg termini per a una companyia específica (SGC) que participa en un mercat liberalitzat organitzat en un pool. Els objectius de la tesi són: modelitzar aquest problema, i desenvolupar i implementar tècniques apropiades i eficients que el resolguin. Un planificació òptima a llarg termini és important, per exemple, per a la confecció de pressupostos, o per a la gestió de compres/consum de combustibles. Una altra aplicació és la de guiar la planificació a curt termini perquè aquesta tingui en compte decisions preses sota una òptica de llarg termini. La nostra proposta per a fer la planificació de la generació és optimitzar la generació esperada de cada unitat (o la unió de diverses unitats de característiques semblants) del pool per a cada interval en que dividim el llarg termini. El model bàsic per la planificació de la generació a llarg termini (LTGP) maximitza el benefici de totes les unitats del pool. La constricció més important és la satisfacció de la demanda, ja que el sistema està sempre balancejat. Utilitzem la formulació de Bloom i Gallant, la qual modela la càrrega a través d'una monòtona de càrrega per cada interval i requereix un número exponencial de constriccions lineals de desigualtat, anomenades LMCs. Altres constriccions (lineals) incloses en el model són: garantia de potència, límits en la disponibilitat de combustibles, emissions màximes de CO2 o una quota de mercat mínima per a la SGC. Una extensió d'aquest model és la planificació conjunta de l'assignació de manteniments de les unitats tèrmiques d'una SGC amb la planificació de la generació. El model conjunt és un problema quadràtic amb variables binàries i contínues. Per resoldre aquest model es proposa un parell d'heurístiques i s'ha implementat un prototipus de branch and bound en AMPL.Aquesta tesi també proposa una manera per coordinar el model LTGP proposat amb una planificació a curt termini. Es desenvolupa un model de curt que inclou els resultats de llarg termini. Donat que el model de planificació a llarg termini s'ha de resoldre sovint (principalment per passar informació acurada al model de curt), les tècniques emprades per a resoldre'l han de donar resultats fiables en un espai de temps curt. Les tècniques aplicades han estat:· Donat que les constriccions de recobriment i les fites de no negativitat defineixen un políedre convex els vèrtexs del qual són fàcils de trobar el model es transforma i les variables esdevenen els coeficients convexos que defineixen un punt. Aquest nou problema es resolt amb l'algoritme de Murtagh i Saunders, que és un procediment òptim. Aquest algoritme s'aplica sota un esquema de generació de columnes donat que el número de vèrtexs del políedre és comparable al número de constriccions. L'avantatge d'aquest mètode és que els vèrtexs es van generant a mesura que es necessiten.· L'aplicació de mètodes directes és computacionalment costós donat el número exponencial de LMCs. De totes maneres, a l'òptim només un conjunt reduït de constriccions de recobriment seran actives. Hem desenvolupat una heurística, anomenada heurística GP, la qual genera un subconjunt de constriccions, entre les quals hi ha les LMCs que són actives a l'òptim. L'heurística resol una seqüència de problemes quadràtics, els quals incrementen el número de LMCs considerades a cada iteració. Els problemes es resolen amb mètodes de punt interior que s'inicialitzen amb tècniques de warm start per tal d'accelerar la convergència cap a la nova solució. Aquest procediment resulta ser molt més eficient que el de generació de columnes. La modelització i els casos de prova estan basats en dades d'un sistema de pool pur i de mercat com ha estat a Espanya fins el juliol de 2006.This thesis presents an approach to the long-term planning of power generation for a company (SGC) participating in a liberalized market organized as a pool. The goal of this thesis is two-fold: to model the problem and to develop and implement appropriate and efficient techniques for solving it.The optimization of the long-term generation planning is important for budgeting and planning fuel acquisitions, and to give a frame where to fit short-term generation planning.Our proposal for planning long-term generation is to optimize the expected generation of each unit (or the merger of several units of the same type) in the power pool over each interval into which the long-term horizon is split.The basic model for long-term generation planning (LTGP) maximizes the profit for all the units participating in the pool. The most important constraint is matching demand, since the market always clears. The Bloom and Gallant formulation is used, which models the load with a load-duration curve for each interval and requires an exponential number of linear inequality constraints, called herein LMCs. Other (linear) constraints included in the model are: minimum generation time, limits on the availability of fuel, maximum CO2 emission limits or the market share of the SGC. This thesis also proposes the way in which coordination between the LTGP model developed and a short-term plan should be considered and provides a model for short-term electrical power planning adapted to the LTGP proposed and which includes the long-term results.Another decision that needs to be taken from a long-term point of view is the joint scheduling of thermal unit maintenances with the generation planning of a particular SGC. The results of a prototype of a Branch and Bound implemented in AMPL are included in this thesis.Long-term planning needs to be considered before short-term planning and whenever the real situation deviates from the forecasted parameters, so the techniques implemented must be efficient so as to provide reliable solutions in a short time. Two methods for handling the LMCs are proposed and compared:● A decomposition technique exploits the fact that the LMCs plus the non-negativity bounds define a convex polyhedron for each interval whose vertices are easy to find. Thus, the problem is transformed and the variables become the coefficients of a convex combination of the vertices. The transformed problem is quadratic with linear constraints, making it suitable to be solved with the Murtagh & Saunders algorithm, which gives an optimal solution. A column-generation approach is used because the number of vertices of the polyhedron is comparable to the number of LMCs. The advantage of this method is that it does not require previous computation of all of the vertices, but rather computes them as the algorithm iterates.● The application of direct methods is computationally difficult because of the exponential number of inequality LMCs. However, only a reduced subset of LMCs will be active at the optimizer. A heuristic, named GP heuristic, has been devised which is able to find a reduced set of LMCs including those that are active at the optimizer. It solves a sequence of quadratic problems in which the set of LMCs considered is enlarged at each iteration. The quadratic problems are solved with an interior point method, and warm starts are employed to accelerate the solution of the successively enlarged quadratic problems. This procedure is more efficient than the column generation one.The modeling and tests of this thesis are based on the pure pool system and market data from the Spanish system up to July 2006

Medium-term power planning in electricity markets with renewable generation sources

The problem addressed in this thesis is the medium-term generation planning over a yearly horizon of a generation company participating in a liberalized electricity market with pool auction of generation and consumption and with bilateral contracts between generation companies and distributions companies or big consumers. It is assumed that the generation portfolio of several generation companies includes a significant proportion of dispatchable renewables (hydro generation with storage reservoirs and pumping schemes) and non-dispatchable renewables as wind power and solar photovoltaic generation. It is also assumed than more than one generation company are able to influence market-price levels through their bidding in the auction so that the market could be oligopolistic. The results obtained are of interest to price-maker generation companies, but also to price-taker generators, and to the market operator to check whether the participants in the market behave as a cartel or seeking an equilibrium. The stochasticity of parameters in the medium-term planning is modeled in two ways. Regarding consumers load and generation unit outages, through the use of the probabilistic method of load matching: by representing the load through predicted load-duration curves of each period into which the yearly horizon is subdivided, by considering the capacity and an outage probability of each generation unit and by using the existing convolution techniques and the linear-inequality load-matching constraints. Regarding renewable energy sources, stochastic programming is used. Hydro-generation scenarios of inflows are developed for each period. As for non-dispatchable renewables (wind power and solar photo-voltaic generation), a novel model of representing them through two pseudo-units: one base unit with small outage probability and a crest unit with large outage probability is proposed, and scenarios are developed for the relevant parameters of the pseudo-units. The solar photo-voltaic generation model requires splitting each period into three subperiods with the dark hours, with the medium-light hours and with the bright hours. Quasi-Monte Carlo techniques have been employed to create a large scenario fan later reduced to a scenario tree with a reduced number of scenarios. Market prices are taken into account through an endogenous linear market-price function of load duration whose intercept depends on total hydro generation level and on wind power and solar photovoltaic level in each node of the scenario tree. With such market price function, the endogenous cartel solution and the equilibrium solutions to the medium-term planning can be obtained. To avoid having to consider the total exponential number of load-matching constraints, a load matching heuristic has been employed where small batches of new load matching constraints are generated after successive optimizations considering only the generated load matching constraints. For equilibrium solutions, the Nikaido-Isoda relaxation algorithm of successive solutions is employed using the successive optimizations of the load-matching heuristic. In mixed-market systems with auction and bilateral contracts, a time-share hypothesis is formulated and the profits function for generation companies with the generation left after honoring their bilateral contracts is formulated. The profit function obtained is non-convex, and a direct global optimization solver was tried, but proved not to be practical for the size of problem to be solved. A non-linear interior-point constrained optimization solver, also employed for problems in pure pool markets, was tried with several special techniques to circumvent the troubles caused by the non-convexity of the objective function and satisfactory results were obtained. A novel model of multi-period medium-term pumping was presented and employed. Results for several realistic test cases having different generation settings have been presented and analyzed.El problema adreçat en aquesta tesi és el de la planificació a mig termini de la generació elèctrica d'una companyia que participa dins d'un mercat elèctric. S'ha assumit que aquestes companyies generadores disposen d'una proporció significant d'energies renovables despatxables (com la generació hidràulica amb embassaments d'emmagatzematge i sistemes de bombeig) i d'energies renovables no-despatxables tals com l'energia eòlica i la generació d'energia solar fotovoltaica. També s’ha tingut en compte que més d'una companyia generadora és capaç d'influir en els nivells de preu de mercat a través de les seves ofertes dins de la subhasta tractant-se, doncs, d'un mercat oligopolístic. Els resultats obtinguts són interessants per a companyies generadores del tipus 'price-maker', però alhora també ho són per companyies 'price-taker' i, finalment, també ho són per a l'operador del mercat per tal de comprovar si els participants en el mercat es comporten com si hi hagués 'cartel' o si bé busquen l'equilibri. L'estocasticitat de la càrrega i les panes de les unitats de generació dins de la planificació a mig termini es modela mitjançant l'ús del mètode probabilístic de recobriment de la càrrega: tot representant la càrrega a través de corbes predites de durada de la càrrega per a cada període tractat, utilitzant tècniques existents de convolucions i les anomenades constriccions de recobriment de la càrrega que són de desigualtat i lineals. Pel que fa a les energies renovables s'ha emprat programació estocàstica. Per a cada període s'han desenvolupat escenaris d'hidràulica per a les aportacions naturals d'aigua. Pel que fa a les renovables no-despatxables (eòlica i solar), es presenta un nou model per a representar-les a través de dues pseudo-unitats: una unitat de base amb una probabilitat de pana molt petita i una unitat de cresta amb una probabilitat de pana gran. La generació solar requereix un model més complex ja que s'han dividit les hores solars en tres subperíodes: sense sol, sol mig i sol. També s'han creat escenaris per als paràmetres més rellevants d'aquestes pseudo-unitats. S'han emprat mètodes de Quasi-Monte Carlo per a crear un gran arbre d'escenaris de tipus FAN que, posteriorment, s'ha reduït a un arbre d'escenaris d'una determinada mida. La funció de preu de mercat respecte a la durada de la càrrega és una funció endògena on es té en compte la variació observada del nivell dels preus amb la generació hidràulica, la generació eòlica i la solar a cada node dins de l'arbre d'escenaris. Amb aquest tipus de funció de preu de mercat, les solucions de cartel i les d'equilibri poden ser obtingudes. Per tal de no haver de considerar un nombre exponencial de constriccions de recobriment, s'utilitza una heurística on petits subconjunts de restriccions es van generant després de successives optimitzacions considerant només les constriccions de recobriment generades. Per a les solucions d'equilibri, s'ha utilitzat l'algoritme de relaxació de Nikaido-Isoda en les successives optimitzacions de l'heurística. Pels mercats mixtos (amb subhasta i contractes bilaterals) s'ha formulat una hipòtesi de 'time-share' i s’ha presentat una funció de beneficis de les empreses generadores on només es té en compte la generació que resta després d'haver satisfet els contractes bilaterals. La funció obtinguda és no convexa i s'ha utilitzat un resolutor d'optimització global, però s'ha vist que no era pràctic per a la mida del problema que s'estava solucionant. Per aquest motiu, s'ha utilitzat un resolutor no lineal de punt interior (Ipopt) amb diverses tècniques especials per tal d'eludir els problemes causats per la no convexitat de la funció objectiu tot obtenint resultats satisfactoris. Finalment, s'ha presentat i s'ha utilitzat un nou mètode per introduir els esquemes de bombeig multi-període i a mig termini. Es mostren i s'analitzen els resultats obtinguts per a diversos casos de prova (realistes) amb diferents configuracions de generació

6th Annual Focus on Creative Inquiry Poster Forum Program

The poster forum today displays a few of the more than 400 projects initiated by Clemson University Creative Inquiry teams. What is Creative Inquiry? It is small-group learning for all students. It is the imaginative combination of engaged learning and undergraduate research. Ultimately, it is the creation of an Ah-ha! Moment - and it is unique to Clemson University. Creative Inquiry establishes small teams of undergraduate students that work with faculty mentors to take on problems that spring from their own curiosity, from a professor\u27s challenge, or from the pressing needs of the world around them. Students take ownership of their projects. They ask questions, they take risks, and they get answers

Dynamic modelling of generation capacity investment in electricity markets with high wind penetration

The ability of liberalised electricity markets to trigger investment in the generation capacity required to maintain an acceptable level of security of supply risk has been - and will continue to be - a topic of much debate. Like many capital intensive industries, generation investment suffers from long lead and construction times, lumpiness of capacity change and high uncertainty. As a result, the ‘boom-and-bust’ investment cycle phenomenon, characterised by overcapacity and low prices, followed by power shortages and high prices, is a prominent feature in the debate. Modelling the dynamics of generation investment in market environments can provide insights into the complexities involved and address the challenges of market design. Further, many governments who preside over liberalised energy markets are developing policies aimed at promoting investment in renewable generation. Of particular interest is the mix and amount of generation investment over time in response to policies promoting high penetrations of variable output renewable power such as wind. Consequently, improved methods to calculate expected output, costs and revenue of thermal generation subject to varying load and random independent thermal outages in a power system with a high wind penetration are needed. In this interdisciplinary project engineering tools are applied to an economic problem together with knowledge from numerous other disciplines. A dynamic simulation model of the aggregated Great Britain (GB) generation investment market has been developed. Investment is viewed as a negative feedback control mechanism with current and future energy prices acting as the feedback signal. Other disciplines called upon include the use of stochastic processes to address uncertainties such as future fuel prices, and economic theory to gain insights into investor behaviour. An ‘energy-only’ market setting is used where generation companies use a classical NPV approach together with the Value at Risk criterion for investment decisions. Market price mark-ups due to market power are also accounted for. The model’s ability to simulate the market trends witnessed in GB since early 2001 is scrutinised with encouraging findings reported. A reasonably good agreement of the model with reality, gives a degree of confidence in the realism of future projections. An advancement to the dynamic model to account for expected high wind penetrations is also included. Building on the initial model iteration, the short-term energy market is simulated using probabilistic production costing based on theMix of Normals distribution technique with a residual load calculation (load net of wind output). Wind speed measurement data is combined with the outputs of atmospheric models to assess the availability of the GB wind resource and its relationship with aggregate load. Simulation results for 2010-40 suggest that the GB system may experience increased generation adequacy risk during the mid to late the 2020s. In addition, many new investments are unable to recover their fixed costs. This triggered an investigation into the design of a capacity mechanism within the context of the modelling environment. In light of the ongoing GB market electricity market reform debate, two mechanisms are tested; a strategic reserve tender and a marketwide capacity market. The goal of these mechanisms is to mitigate generation adequacy risk concerns by achieving a target winter peak de-rated capacity margin

Towards a Greater Britain: a political biography of Oswald Mosley, 1918-1947

This thesis examines the major stages in the political career of Oswald Mosley and argues that a continuity existed in his diagnosis of contemporary history from the moment he entered political life at the end of the First World War as a zealous parliamentarian till his last days as an unrepentant fascist. An ideal type of the 'esoteric' core of Mosley's ideology is used to identify a consistent thread which resolves the contradictions in Mosley's political agitations into paradoxes. Drawing on a theory of ideology which distinguishes between its fundamental and operative dimensions, Mosley's core (fundamental) ideology is depicted ideal typically as the ambition to realize Bntain's potential for national greatness conceived in a future oriented, modernizing rather than a nostalgic or conservative perspective. The structure of the biography follows the chronological narrative of Mosley's life, episodically, illuminating it through pivotal moments in his career. Through a textual and contextual analysis of these moments it identifies the performance of the operative dimension of Mosley's fundamental ideology in order to bring out its internal consistency. Each chapter highlights a theme which may have manifested itself at other moments in Nlosley's life but is especially distinct at one stage of Nlosley's career. These themes are the myth of the airman, leadership, economics, unemployment, the New Party, the nation and Greater Britain, anti-Semitism and violence, philosophical idealism and the philosophy of apologia. The thesis draws on the vast published textual output from Mosley along with reports of his speeches, supported by many contemporary writings relating to chapter topic. These resources are used to demonstrate and shed light on the esoteric mainspring of Mosley's politics. In addition the thesis demonstrates and argues in favour of a biographic methodology which does not construct the inner machinations of the subject's psychology or 'mind' as an explanation of behaviour but looks pragmatically to the significant products of the subject and constructs, ideal typically, a consistent ideological matrix the centre of the subjects politics. This thesis contributes to knowledge of the subject by presenting a pragmatic understanding of Mosley's political motivations and identifying a consistent core to his political pronouncements. The thesis also brings to biographical studies a phenomenological methodology which dispenses with the postulation of a knowable core personality or 'real' psychological life in order to demonstrate the inner coherence of the subject's personality for the purpose of historical reconstruction

Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation: Special Report of the Intergovernmental Panel on Climate Change

This Special Report on Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation (SREX) has been jointly coordinated by Working Groups I (WGI) and II (WGII) of the Intergovernmental Panel on Climate Change (IPCC). The report focuses on the relationship between climate change and extreme weather and climate events, the impacts of such events, and the strategies to manage the associated risks. The IPCC was jointly established in 1988 by the World Meteorological Organization (WMO) and the United Nations Environment Programme (UNEP), in particular to assess in a comprehensive, objective, and transparent manner all the relevant scientific, technical, and socioeconomic information to contribute in understanding the scientific basis of risk of human-induced climate change, the potential impacts, and the adaptation and mitigation options. Beginning in 1990, the IPCC has produced a series of Assessment Reports, Special Reports, Technical Papers, methodologies, and other key documents which have since become the standard references for policymakers and scientists.This Special Report, in particular, contributes to frame the challenge of dealing with extreme weather and climate events as an issue in decisionmaking under uncertainty, analyzing response in the context of risk management. The report consists of nine chapters, covering risk management; observed and projected changes in extreme weather and climate events; exposure and vulnerability to as well as losses resulting from such events; adaptation options from the local to the international scale; the role of sustainable development in modulating risks; and insights from specific case studies