An approach to multi-objective life cycle cost optimization of wind turbine tower structures

Horsthemke, Hagen Wolfgang (2013-12)

Thesis (MEng)-- Stellenbosch University, 2013.

Thesis

ENGLISH ABSTRACT: Support tower structures of Wind Energy Conversion Systems (WECS) are major cost items and by means of integrated design and optimization, the Life-Cycle Cost (LCC) can be reduced substantially. In this thesis, Horizontal Axis Wind Turbine (HAWTs) tower structures are investigated by means of a technique or tool that can bene t in decision making related situations to reduce the LCC of such WECS support towers from inception to disposal. Often, during the conceptual design phase a certain level of uncertainty or fuzziness exists and plays a role. The central focus in this project is on lattice type towers; however an account on tapered, tubular monopole towers is given as well. The problem is identi ed to be of a multi-objective nature, where a variety of criteria or objectives that are identi ed play a role in the possible reduction of the total LCC of the structure. The study also entails the delineation and discussion of the factors and components that a ect the LCC of a steel structure. The decision maker has control over only a few of these factors and components as identi ed, and these can be formulated by means of an objective to be minimized (or maximized in several other cases). Some of the objectives are incommensurable and others are commensurable with each other. In other words, several of these objectives either `compete' or don't `compete' against each other, respectively. The investigation resulted in the development of a multi-objective LCC optimization using the λ-formulation (or min-max formulation) as the objective aggregating approach for the four objectives identi ed (varied during analysis for sensitivity checks). The objectives are user-de ned in terms of membership functions that grade the degree of membership from total acceptance to total rejection by means of boundary values. This formulation is Non-Pareto based and the decision maker obtains the best trade-o or best compromise solution. The detailed discussion around these objectives is included in the literature study. The objectives in the multi-objective study are weight, cost, perimeter and nodal deflections, and a weighting of the objectives is possible but this is excluded from this study. A Genetic Algorithm (GA), coded in MATLAB, is implemented as the optimization tool or technique. The algorithm uses a quadratic penalty function approach and a natively written Finite Element Analysis (FEA) tool is used for the response model in the tness evaluation process, where the performance for stability, capacity and overall deflections of an individual in the population is quanti ed. A GA has the advantage that it operates on an entire population of individuals using basic principles such as genetics, crossover, mutation, selection and survival of the ttest from biology and Darwinian principles. GAs are very robust and e ective global search methods that can be applied to most elds of study. GAs have previously been e ectively applied in structural, single objective optimization (structural weight) problems. The GA is adopted and modi ed and veri ed with results on academic problems obtained from literature. Satisfactory performance was observed, although room for improvement is identi ed. A case study on a full scale model is performed, using circular hollow sections and equal leg angle sections. These are commonly used steel profi les for lattice type towers. The results obtained are as expected. The structural mass was used as a measure to compare the results. A heavier structure is obtained using the equal leg angle sections compared to the CHS structure with a di fference of up to 20% in weight. The best compromise solutions are feasible and near optimal, given the conditions of the equally weighted objectives in this study. The membership function defi nition and boundary value determination still remains a key issue when using fuzzy logic to incorporate the preference information of the decision maker.

AFRIKAANSE OPSOMMING: Toringstrukture van windturbines is belangrike kostekomponente van `n windkragopwekking stelsel. Deur middel van geï ntegreerde ontwerp en optimalisering kan die lewensikluskoste aansienlik verminder word. In hierdie tesis word horisontale-as windturbinetoringstrukture ondersoek. Deur middel van `n tegniek of hulpmiddel wat kan baat vind by besluitneming situasies, word die lewensiklus-koste van sodanige windturbine ondersteuning torings vanaf voorgebruik-fase tot lewenseinde-fase verminder. Dikwels, tydens die konseptuele ontwerp-fase, speel `n sekere vlak van onsekerheid of verwarring ook `n rol. Die sentrale fokus in hierdie projek is op staal vakwerk tipe torings gelê. `n Vereenvoudigde ontleeding van buisvormige torings is ook benader. Die probleem is van multikriteria aard, waar `n verskeidenheid van kriterie of doelwitte ge denti seer was. Hulle speel `n rol in die moontlike vermindering van die totale lewensiklus-koste van die struktuur. Die studie behels ook die bespreking en afbakening van die faktore en komponente wat die lewensiklus-koste van 'n staal struktuur bepaal. Die besluitnemer het slegs beheer oor sekere van hierdie faktore en komponente, en hierdie word deur middel van `n saamgevoegde doel-funksie gede neer wat dan geminimeer word. Sommige van die doelfunksies kompeteer met mekaar en sommige kompeteer nie met mekaar nie. Die ondersoek het gelei tot die ontwikkeling van `n multikriteria lewensiklus-koste optimalisering met behulp van die λ-formulering (of min-max formulering). Hierdie is `n tegniek wat die kriterie in vorm van `n verteenwoordigende doel-funksie saamvoeg. Daar is vier doelwitte wat geï denti seer was. Die gebruiker de nieer spesiale, lineêre doel-funksies wat van totale aanvaarding tot totale verwerping streek. Dit word deur middel van randwaardes gedoen. Hierdie formulering is nie Pareto gebaseer nie, en die besluitnemer verkry die `best trade-off ' of die beste kompromis oplossing. Die detailleerde bespreking rondom hierdie doelwitte is in die literatuurstudie ingesluit. Die doelwitte wat in die multikriteria studie gebruik word is gewig, koste, omtrek van die snitpro el en strukturêle defleksie. `n Gewig kan aan elke kriterium toegeken word, maar dit word van hierdie studie uitgesluit. `n Genetiese algoritme (GA), geï mplementeer in MATLAB, word as die optimalisering instrument en tegniek gebruik. Die algoritme gebruik `n kwadratiese `straf-funksie' en `n MATLAB Eindige Element Analise (EEA) word gebruik vir die gedragsmodel in die `fi ksheid' evalueringsproses. Die prestasie vir stabiliteit, kapasiteit en algehele verlegging van `n individu in die GA bevolking word daardeur gekwanti seer. `n GA het die voordeel, dat dit met `n hele bevolking van individue werk. Dit is gebaseer op beginsels van genetika en Darwin se beginsels. GAs is baie stabiel en ook e ektiewe globale soek metodes wat van toepassing in verskillende studierigtings is. GAs is al e ektief toegepas in strukturêle optimalisering (veral strukturêle gewig optimalisiering). Die GA in hierdie studie was aangepas en die gedrag en prestasie is bevestig met resultate van akademiese probleme uit die literatuur. Bevredigende prestasie is waargeneem, maar ruimte vir verbetering is ook geï denti seer. `n Gevallestudie oor `n grootskaal model is uitgevoer, en die gebruik van ronde holpro ele en gelykbenige hoekpro ele is uitgevoer. Dit is algemeen gebruikte staalpro ele vir vakwerk tipe torings. Die resultate wat verkry is, is soos verwag. Die strukturêle massa is gebruik as `n maatstaf om die resultate te vergelyk. `n Swaarder struktuur is die resultaat wanneer gelykbenige hoekpro ele gebruik word in vergelyking met die ronde holpro el struktuur. `n Verskil tot 20% in gewig is waargeneem. Die beste kompromis oplossing is haalbaar en naby-optimaal, gegewe die omstandighede van die gelyk geweegde doelfunksies in hierdie studie. Die doel-funksie de nisie, die voorkeur van die besluitnemer en die bepaling van die randwaardes bly steeds `n belangrike kwessie by die gebruik van hierdie benadering.

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