We are currently witnessing a rapid expansion of renewable power production, an increase dominated by wind and solar power. These intermittent energy sources, while having low production costs, increases the uncertainty on the electrical markets. Hydropower is a renewable source of electricity that is capable of controlled production. It is assumed that hydropower will take a more central role in terms of balancing deficiencies caused by intermittent sources. In this thesis, we present a detailed model of a single hydropower plant consisting of 𝑛 turbines. This model is then used as input of solving the optimisation problem of revenue maximisation for the hydro plant owner. The model used takes into account head effects as well as stochastic inflow of water and the stochastic fluctuations of electricity prices.

Hydropower systems often contain complex river systems which cause the simulations and analyses of a hydropower operation to be computationally heavy. The complex river system is referred to as something called a Detailed model. By creating a simpler model, denoted the Equivalent model, the computational issue could be circumvented. The purpose of this Equivalent model is to emulate the results of the Detailed model. This thesis computes the Equivalent model for a large hydropower system using Particle Swarm Optimisation- algorithm, then evaluates the Equivalent model performance. Simulations are performed on ten rivers in Sweden, representing four trading areas for one year, October 2017 – September 2018. Furthermore, the year is divided into Quarterly and Seasonal periods, to investigate whether the Equivalent model changes over time. The Equivalent model performance is evaluated based on the relative power difference and computational time compared to the Detailed model. The relative power difference is 4%23% between Equivalent and Detailed models, depending on the period and trading area, with the computational time can be reduced by more than 90%. Furthermore, the Equivalent model changes over time, suggesting that when the year is divided appropriately, the Equivalent model could perform better. The relative power difference results indicate that the Equivalent model performance can still be improved by dividing the periods more appropriately, other than Quarterly or Seasonal. Nevertheless, the results provide a satisfactory Equivalent model, based on the faster computation time and a reasonable relative power difference. Finally, the Equivalent model could be used as a foundation for further analyses and simulations. / Vattenkraftsystem består ofta av komplexa älvsystem som gör att simuleringar och analyser av vattenkraftens operation blir beräkningsmässigt tunga. Det komplexa älvsystem kallas en Detaljeraded modell. Genom att skapa en enklare modell, betecknas som en Ekvivalent modell, beräkningsproblemen kan kringgås. Syftet med denna Ekvivalenta modell är att emulera resultaten av den komplexa Detaljerade modellen. Detta examensarbete beräknar den Ekvivalenta modellen för ett stort vattenkraftssystem med hjälp av Particle Swarm Optimisation- algorithmen, och utvärderar modellprestandan hos Ekvivalenten. Simuleringar utförs på tio älvar i Sverige, som representerar fyra handelsområden under ett år, från oktober 2017 september 2018. Dessutom är året uppdelat i kvartals- och säsongsperioder för att undersöka om den Ekvivalenta modellen förändras över tid. Denna Ekvivalenta modell utvärderas baserat på den relativa effektskillnaden och beräkningstiden jämfört med den Detaljerade modellen. Den relativa effektskillnaden är 4% 23% mellan de Ekvivalenta och Detaljerade modellerna, beroende på period och handelsområde, och beräkningstiden minskas med mer än 90%. Vidare ändras Ekvivalenta modellen över tiden, vilket tyder på att när året delas upp på rätt sätt kan den Ekvivalenta modellen prestera ännu bättre. De relativa effektskillnaderna indikerar att vissa perioder fortfarande kan förbättras genom att dela upp perioden mer korrekt. Trots allt, förser resultanten en tillfredsställande Ekvivalent modell som har en mer effektiv beräkningstid och rimliga effektskillnader. Slutligen skulle den Ekvivalenta modellen kunna användas som en grund för ytterligare analyser och simuleringar.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-05-10T12:15:28Z No. of bitstreams: 1 alexandredasilvafernandes.pdf: 3326554 bytes, checksum: f4dfcfe70bde99c5ebe4501f03add83e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-05-22T15:33:53Z (GMT) No. of bitstreams: 1 alexandredasilvafernandes.pdf: 3326554 bytes, checksum: f4dfcfe70bde99c5ebe4501f03add83e (MD5) / Made available in DSpace on 2018-05-22T15:33:53Z (GMT). No. of bitstreams: 1 alexandredasilvafernandes.pdf: 3326554 bytes, checksum: f4dfcfe70bde99c5ebe4501f03add83e (MD5) Previous issue date: 2018-02-20 / O planejamento da operação do Sistema Interligado Nacional constitui-se uma tarefa de alta complexidade, seja pela quantidade acentuada de usinas hidrelétricas e termelétricas distribuídas nos quatro submercados interligados, ou pelas características marcantes da operação das hidrelétricas, no que diz respeito às incertezas dos cenários hidrológicos futuros e aos acoplamentos espacial e temporal. O objetivo deste planejamento é a determinação de uma política ótima de despacho das usinas do sistema de modo a minimizar o valor esperado dos custos operativos no horizonte considerado. Uma importante restrição do problema é o suprimento da demanda de energia elétrica, dado pela diferença entre a carga efetiva de cada submercado e a geração das usinas não simuladas, esta última composta pela energias alternativas (eólica, solar, biomassa), pequenas centrais hidrelétricas, entre outros. Entretanto, a crescente penetração da geração renovável, aliada às incertezas das fontes naturais como eólica e solar (pois dependem de fatores climáticos e por isso são imprevisíveis), contribui com a necessidade de representação da demanda em diversos cenários para um correto despacho das usinas e uma operação do sistema mais confiável. Sabendo que os modelos oficiais atuais tratam apenas as incertezas oriundas dos cenários hidrológicos, devido à dificuldade de implementação e alocação de memória na consideração de outras incertezas na Programação Dinâmica Dual Estocástica, o trabalho desenvolvido nesta dissertação propõe metodologias que incluem os diversos cenários de demanda, além de representar com maior detalhe a geração das hidrelétricas. Além disso, são propostos algoritmos de representação analítica da Função de Custo Imediato em sistemas isolados e com múltiplas áreas na busca por uma redução das dimensões do problema tratado. Finalmente, são realizados testes em sistemas tutorias e os resultados são analisados para avaliar as performances computacionais das metodologias propostas. / The operation schedulling of Brazilian System constitutes a task of high complexity, either due to the large number of hydro and thermal plants distributed in the four interconnected submarkets, or due to the outstanding characteristics of the hydro plants, with respect to the uncertainties in the hydrological scenarios future and due to spatial and temporal couplings. The objective of this planning is the determination of an optimal dispatch policy of plants that minimizes the expected value of the operating costs in the considered horizon. An important constraint is the supply of demand, which is obtained by the difference between the effective load of each submarket and the generation of non-simulated plants, composed of renewable energies (wind, solar, biomass), small hydropower plants, and others. However, the growing penetration of renewable generation, coupled with the uncertainties of natural sources such as wind and solar (because they depend on climatic factors and are therefore unpredictable), contributes to the need to represent demand in different scenarios for a correct dispatch of the plants and a more reliable system operation. Knowing that the current official models deal only with the uncertainties arising from the hydrological scenarios, due to the difficulty of implementation and memory allocation in the consideration of other uncertainties in Stochastic Dual Dynamic Programming, this work proposes methodologies that include the several scenarios demand, besides representing in greater detail the generation of hydroelectric plants. In addition, algorithms are proposed for analytical representation of the Immediate Cost Function in isolated systems with multiple areas in the search for a reduction of the dimensions of the problem. Finally, tests are performed on tutorial systems and the results are analyzed to evaluate the computational performances of the proposed methodologies.