MSc (Statistics) / Department of Statistics / Generally, short term load forecasting is essential for any power generating utility. In this dissertation the main objective was to develop short term load forecasting models for the peak demand periods (i.e. from 18:00 to 20:00 hours) in South Africa using. Quantile semi-parametric additive models were proposed and used to forecast electricity demand during peak hours. In addition to this, forecasts obtained were then used to nd an optimal number of generating units to commit (switch on or o ) daily in order to produce the required electricity demand at minimal costs. A mixed integer linear programming technique was used to nd an optimal number of units to commit. Driving factors such as calendar e ects, temperature, etc. were used as predictors in building these models. Variable selection was done using the least absolute shrinkage and selection operator (Lasso). A feasible solution to the unit commitment problem will help utilities meet the demand at minimal costs. This information will be helpful to South Africa's national power utility, Eskom. / NRF

<p>In the US, seven regional transmission organizations (RTOs) operate wholesale electricity markets within three largely independent transmission systems, the largest of which includes five RTO regions and many vertically integrated utilities.</p> <p>RTOs operate a day-ahead and a real-time market. In the day-ahead market, generation and demand-side resources are optimally scheduled based on bids and offers for the next day. Those schedules are adjusted according to actual operating conditions in the real-time market. Both markets involve a unit commitment calculation, a mixed integer program that determines which generators will be online, and an economic dispatch calculation, an optimization determines the output of each online generator for every interval and calculates locational marginal prices (LMPs).</p> <p>The use of LMPs for the management of congestion in RTO transmission systems has brought efficiency and transparency to the operation of electric power systems and provides price signals that highlight the need for investment in transmission and generation. Through this work, we aim to extend these efficiency and transparency gains to the coordination across RTOs. Existing market-based inter-regional coordination schemes are limited to incremental changes in real-time markets. </p> <p>We propose a multi-regional unit-commitment that enables coordination in the day-ahead timeframe by applying a distributed approach to approximate a system-wide optimal commitment and dispatch while allowing each region to largely maintain their own rules, model only internal transmission up to the boundary, and keep sensitive financial information confidential. A heuristic algorithm based on an extension of the alternating directions method of multipliers (ADMM) for the mixed integer program is applied to the unit commitment. </p> The proposed coordinated solution was simulated and compared to the ideal single-market scenario and to a representation of the current uncoordinated solution, achieving at least 58% of the maximum potential savings, which, in terms of the annual cost of electric generation in the US, could add up to nearly $7 billion per year. In addition to the coordinated day-ahead solution, we develop a distributed solution for financial transmission rights (FTR) auctions with minimal information sharing across RTOs that constitutes the first known work to provide a viable option for market participants to seamlessly hedge price variability exposure on cross-border transactions.

[pt] O sistema elétrico de potência brasileiro, denominado Sistema Interli- gado Nacional – SIN, possui como órgão responsável pela operação o Op- erador Nacional do Sistema Elétrico – ONS. A fim de utilizar os recursos energéticos de forma a garantir a qualidade, confiabilidade e segurança no suprimento de energia elétrica ao menor custo total de operação, o oper- ador utiliza uma cadeia de modelos de otimização que subsidia a tomada de decisão no Programa Diário de Operação, implementado diariamente nas salas de controle do ONS e de agentes de geração para operação em tempo real. A etapa de Programação Diária do Operador Nacional do Sistema Elétrico busca estabelecer o despacho centralizado da geração e das reser- vas de potência a fim de atender à demanda prevista de energia elétrica considerando os limites da rede elétrica, das tecnologias de geração e a in- certeza de disponibilidade das unidades geradores e linhas de transmissão. Este trabalho propõe um modelo computacional programado em código aberto para a programação diária implementado na linguagem Julia. O modelo pertence à classe de modelos de unit commitment e considera a cootimização do despacho de geração e definição dos níveis de reservas em cada gerador do SIN para atender a critérios de segurança do tipo N − K . / [en] The Brazilian electric power system, called the National Interconnected System - SIN ( Sistema Interligado Nacional), has as its responsible institu- tion for operation the National Electric System Operator - ONS (Operador Nacional do Sistema Elétrico). In order to manage energy resources to en- sure quality, reliability and security of electricity supply at the lowest total operating cost, the operator uses a chain of optimization models that feeds the Daily Operation Program for decision-making, which is implemented everyday in the ONS and generators control rooms for real-time operation. The Daily Scheduling phase of the National Electric System Operator seeks to establish the centralized dispatch of generation and power reserves in order to meet the expected demand for electricity considering the limits of both the electrical grid and the generation technologies, along with the uncertainty of availability of generator units and transmission lines. This work proposes a computational model programmed in open-source for daily operation programming, implemented in the Julia language. The model be- longs to the unit commitment model class and it considers the generation dispatch cooptimization and reserve levels definition in each SIN generator to meet N-K safety criteria.

[pt] Transmission switching já foi apresentado anteriormente como uma ferramenta capaz de prover benefícios significativos na operação de sistemas de potência, como redução de custos e aumento de confiabilidade. Dentro do contexto de mercados co-otimizados para energia e reservas, este trabalho endereça a co-otimização de transmission switching pós-contingência no planejamento da operação de sistemas elétricos. Os modelos propostos para programação diária e despacho econômico diferem de formulações existentes devido à consideração conjunta de três fatores complicadores. Primeiro, ações de transmission switching são consideradas nos estados pré e pós-contingência, portanto requerendo variáveis binárias pós-contingência. Adicionalmente, a programação de geradores e as ações de transmission switching são co-otimizadas. Além disso, a operação de geradores é caracterizada temporalmente em um contexto multi-período. Os modelos propostos são formulados como programas inteiros-mistos desafiadores para os quais os softwares comerciais comumente utilizados para modelos mais simples podem levar à intratabilidade até para instâncias de tamanho moderado. Como metodologia de solução, nós apresentamos uma versão aperfeiçoada de um algoritmo de geração de colunas e restrições aninhado, com a adição de restrições válidas para melhorar o desempenho computacional. Simulações numéricas demonstram o desempenho efetivo da abordagem proposta, assim como suas vantagens econômicas e operacionais sobre modelos existentes que desconsideram o transmission switching pós-contingência. / [en] Transmission switching has been previously shown to offer significant benefits to power system operation, such as cost savings and reliability enhancements. Within the context of co-optimized electricity markets for energy and reserves, this work addresses the co-optimization of post contingency transmission switching in power system operation planning. The proposed models for unit commitment and economic dispatch differ from existing formulations due to the joint consideration of three major complicating factors. First, transmission switching actions are considered both in the preand post-contingency states, thereby requiring binary post-contingency variables. Secondly, generation scheduling and transmission switching actions are co-optimized. In addition, the time coupled operation of generating units is precisely characterized. The proposed models are formulated as challenging mixed-integer programs for which the off-the-shelf software customarily used for simpler models may lead to intractability even for moderatelysized instances. As a solution methodology, we present enhanced versions of an exact nested column-and-constraint generation algorithm featuring the inclusion of valid constraints to improve the overall computational performance. Numerical simulations demonstrate the effective performance of the proposed approach as well as its economic and operational advantages over existing models disregarding post-contingency transmission switching.

Wir betrachten ein Kraftwerkssystem mit thermischen Blöcken und Pumpspeicherwerken und entwickeln dafür ein Modell für den kostenoptimalen Wochenbetrieb. Auf Grund der Ungewißheit des Bedarfs an elektrischer Energie ist das mathematische Modell ein mehrstufiges stochastisches Problem. Dieses Modell beinhaltet viele gemischt-ganzzahlige stochastische Entscheidungsvariablen. Die Variablen einzelner Einheiten sind aber nur durch wenige Nebenbedingungen miteinander verbunden, welches die Zerlegung in stochastische Teilprobleme erleichtert. Diese stochastischen Teilprobleme besitzen deterministische Analoga, deren Lösungsverfahren entsprechend erweitert werden können. In dieser Arbeit werden ein Abstiegsverfahren für stochastische Speicherprobleme und eine Erweiterung der dynamischen Programmierung auf stochastische Probleme betrachtet. Die Lösung des dualen Problems führt zu Schattenpreisen, die bestimmte Einsatzentscheidungen bevorteilen. Die Heuristik zur Suche von primalen zulässigen Punkten wertet eine Folge von zugeordneten Economic-Dispatch-Problemen aus. Die Kombination der Einschränkung auf dual bevorzugte Fahrweisen (Lagrangian reduction) mit der Auswertung einer Folge von Economic-Dispatch-Problemen (Facettensuche) führt zu einem effizienten Verfahren. Die numerischen Ergebnisse an Hand realistischer Daten eines deutschen Versorgungsunternehmens rechtfertigen diesen Zugang. / We consider a power generation system comprising thermal units and pumped hydro storage plants, and introduce a model for its weekly cost-optimal operation. Due to the uncertainty of the load, the mathematical model represents a dynamic (multi-stage) stochastic program. The model involves a large number of mixed-integer (stochastic) decisions but its constraints are loosely coupled across operating power units. The coupling structure is used to design a stochastic Lagrangian relaxation method, which leads to a decomposition into stochastic single unit subproblems. The stochastic subproblems have deterministic counterparts, which makes it easy to develop algorithms for the stochastic problems. In this paper, a descent method for stochastic storage problems and an extension of dynamic programming towards stochastic programs are developed. The solution of the dual problem provides multipliers leading to preferred schedules (binary primal variables). The crossover heuristics evaluates the economic dispatch problems corresponding to a sequence of such preferred schedules. The combination of the restriction on dual preferred schedules (Lagrangian reduction) with the evaluation of a sequence (facet search) leads to an efficient method. The numerical results on realistic data of a German utility justify this approach.

This dissertation focuses on selected issues in regard to the mathematical modeling of electricity markets. In a first step the interrelations of electric power market modeling are highlighted a crossroad between operations research, applied economics, and engineering. In a second step the development of a large-scale continental European economic engineering model named ELMOD is described and the model is applied to the issue of wind integration. It is concluded that enabling the integration of low-carbon technologies appears feasible for wind energy. In a third step algorithmic work is carried out regarding a game theoretic model. Two approaches in order to solve a discretely-constrained mathematical program with equilibrium constraints using disjunctive constraints are presented. The first one reformulates the problem as a mixed-integer linear program and the second one applies the Benders decomposition technique. Selected numerical results are reported.

Fundação de Apoio a Pesquisa e à Inovação Tecnológica do Estado de Sergipe - FAPITEC/SE / The growth of the electric energy consumption in the last years has generated the need of the increase in the amount of power sources, making the electricity sector undergo some large changes. This has provided the search for tools that promotes a better efficiency and security to the electrical power systems. A planning problem that is considered important in the daily operation of the power systems is the Unit Commitment, where the time schedule of the operation is defined, determining which machines will be online or offline, and which are the operating points. Those units must operate by load variation, respecting the operative and security constraints. This research proposes the resolution of the problem for the short-term planning, taking a set of constraints associated with the thermal generation and the power system. Among them, we can highlight the output power variation constraints of the machines and the security restrictions of the transmission system, avoided in most Unit Commitment studies. This problem is nonlinear, mixed-integer and has a large scale. The methodology used involves the utilization of an Adaptive Genetic Algorithm, for the Unit Commitment problem, and the Interior-Point Primal- Dual Predictor–Corrector Method, for DC power flow resolution in economic dispatch problem. Furthemore, this research proposes the implementation of cross-over and mutation operators of Genetic Algorithm based on a ring methodology applied in Unit Commitment matrix. The results were obtained through simulations in a mathematical simulation software, using the IEEE test systems with 30 bus and 9 generators, and another with 24 bus and 26 generators. The validation of the algorithm was done by comparing the results with other works in the literature. / O crescimento do consumo de energia elétrica nos últimos anos vem gerando a necessidade de um aumento na quantidade de fontes geradoras, fazendo com que o setor elétrico passe por grandes mudanças. Isso tem proporcionado a busca por ferramentas que ofereçam maior eficiência e segurança aos sistemas de potência. Um problema considerado de extrema importância na operação diária dos sistemas elétricos é o planejamento da Alocação das Unidades Geradoras, onde define-se a programação horária das unidades do sistema, determinando quais máquinas deverão estar ligadas ou desligadas, e quais serão seus respectivos pontos de operação. Essas unidades geradoras devem operar de forma eficaz, mediante a variação da carga, respeitando restrições operativas e de segurança do sistema. Este trabalho propõe a resolução do problema para o planejamento de curto prazo, levando em consideração uma série de restrições relacionadas a geração térmica e ao sistema elétrico. Entre elas, podemos destacar as restrições de variação de potência de saída das máquinas e as restrições de segurança do sistema de transmissão, evitadas na maioria dos estudos de Alocação de Unidades Geradoras. Este problema tem característica não-linear, inteiro-misto e de grande escala. A metodologia utilizada para resolução do problema envolve a utilização de um Algoritmo Genético Adaptativo, para Alocação das Unidades, e o Método de Pontos Interiores Primal-Dual Preditor-Corretor, para a resolução do Fluxo de Potência Ótimo DC no problema do Despacho Econômico. Além disso, este trabalho propõe a implementação dos operadores de cross-over e mutação do Algoritmo Genético com base em uma metodologia anelar aplicada na matriz de alocação de unidades. Os resultados foram obtidos através de simulações em um software de simulação matemática, utilizando os sistemas testes do IEEE de 30 barras com 9 geradores e 24 barras com 26 geradores, e a validação do algoritmo foi feita comparando os resultados obtidos com os outros trabalhos da literatura.

Cette thèse comporte des résultats théoriques et pratiques sur deux métaheuristiques, la Recherche Dispersée et la Recherche Voisinage variable (RVV), ainsi que sur des Matheuristiques. Au niveau théorique, la contribution principale de cette thèse est la proposition d’un algorithme de recherche dispersée avec l’arrondi directionnel convergent pour les programmes en nombres entiers mixtes (0-1 MIP), avec une preuve de cette convergence en un nombre fini d’itérations. En se basant sur cet algorithme convergeant, deux implémentations et plusieurs heuristiques sont proposées et testées sur des instances de 0-1 MIP. Les versions testées reposent sur des implémentations non optimisées pour mettre en évidence la puissance des approches dans une forme simplifiée. Nos résultats démontrent l’efficacité de ces approches initiales, ce qui les rend attractives lorsque des solutions de très haute qualité sont recherchées avec un investissement approprié en termes d’effort de calcul. Cette thèse inclut également quelques nouvelles variantes de la métaheuristique Recherche Voisinage Variable telles qu’une recherche voisinage variable deux niveaux, une recherche voisinage variable imbriquée, une descente voisinage variable cyclique et une heuristique de plongée voisinage variable. En outre, plusieurs implémentations efficaces de ces algorithmes basés sur la recherche voisinage variable ont été appliquées avec succès à des problèmes NP-Difficiles apparaissant en transport, logistique, production d’énergie, ordonnancement, et segmentation. Les heuristiques proposées se sont avérées être les nouvelles heuristiques de référence sur tous les problèmes considérés. La dernière contribution de cette thèse repose sur la proposition de plusieurs matheuristiques pour résoudre le problème de Conception de Réseau Multi-flots avec Coût fixe (CRMC). Les performances de ces matheuristiques ont été évaluées sur un ensemble d’instances de référence du CRMC. Les résultats obtenus démontrent la compétitivité des approches proposées par rapport aux approches existantes de la littérature. / This thesis consists of results obtained studying Scatter Search, Variable Neighbourhood Search (VNS), and Matheuristics in both theoretical and practical context. Regarding theoretical results, one of the main contribution of this thesis is a convergent scatter search with directional rounding algorithm for 0-1 Mixed Integer Programs (MIP) with the proof of its finite convergence. Besides this, a convergent scatter search algorithm is accompanied by two variants of its implementation. Additionally, several scatter search based heuristics, stemming from a convergent scatter search algorithm have been proposed and tested on some instances of 0-1 MIP. The versions of the methods tested are first stage implementations to establish the power of the methods in a simplified form. Our findings demonstrate the efficacy of these first stage methods, which makes them attractive for use in situations where very high quality solutions are sought with an efficient investment of computational effort.This thesis also includes new variants of Variable Neighborhood Search metaheuristic such as a two-level variable neighborhood search, a nested variable neighborhood search, a cyclic variable neighborhood descent and a variable neighborhood diving. Additionally, several efficient implementation of those variable neighborhood search algorithms have been successfully applied for solving NP-Hard problems appearing in transportation, logistics, power generation, scheduling and clustering. On all tested problems, the proposed VNS heuristics turned out to be a new state-of-the art heuristics. The last contribution of this thesis consists of proposing several matheuristics for solving Fixed-Charge Multicommodity Network Design (MCND) problem. The performances of these matheuristics have been disclosed on benchmark instances for MCND. The obtained results demonstrate the competitiveness of the proposed matheuristics with other existing approaches in the literature.

This dissertation focuses on selected issues in regard to the mathematical modeling of electricity markets. In a first step the interrelations of electric power market modeling are highlighted a crossroad between operations research, applied economics, and engineering. In a second step the development of a large-scale continental European economic engineering model named ELMOD is described and the model is applied to the issue of wind integration. It is concluded that enabling the integration of low-carbon technologies appears feasible for wind energy. In a third step algorithmic work is carried out regarding a game theoretic model. Two approaches in order to solve a discretely-constrained mathematical program with equilibrium constraints using disjunctive constraints are presented. The first one reformulates the problem as a mixed-integer linear program and the second one applies the Benders decomposition technique. Selected numerical results are reported.

[pt] Esta dissertação está estruturada como uma coleção de cinco artigos formatados em capítulos. Os quatro primeiros artigos apresentam contribuições em modelagem e metodológicas para problemas de operação ou investimento em sistemas de potência usando arcabouço de otimização robusta adaptativa e modificações no algoritmo de geração de linhas e colunas (CCGA). O primeiro artigo aborda a programação de curto prazo com restrição de segurança, onde a resposta automática de geradores é considerada. Um modelo robusto de dois estágios é adotado, resultando em complexas instâncias de programação inteira mista, que apresentam variáveis binárias associadas às decisões de primeiro e segundo estágios. Um novo CCGA que explora a estrutura do problema é desenvolvido. O segundo artigo usa redes neurais profundas para aprender o mapeamento das demandas nodais aos pontos de ajuste dos geradores para o problema do primeiro artigo. O CCGA é usados para garantir a viabilidade da solução. Este método resulta em importantes ganhos computacionais em relação ao primeiro artigo. O terceiro artigo propõe uma abordagem adaptativa em dois estágios para um modelo robusto de programação diária no qual o conjunto de incerteza poliedral é caracterizado diretamente a partir dos dados de geração não despachável observados. O problema resultante é afeito ao CCGA. O quarto artigo propõe um modelo de dois estágios adaptativo, robusto em distribuição para expansão de transmissão, incorporando incertezas a longo e curto prazo. Um novo CCGA é desenvolvido para lidar com os subproblemas. Finalmente, sob uma perspectiva diferente e generalista, o quinto artigo investiga a adequação de prêmios de incentivo para promover inovações em aspectos teóricos e computacionais para os desafios de sistemas de potência modernos. / [en] This dissertation is structured as a collection of five papers formatted as chapters. The first four papers provide modeling and methodological contributions in scheduling or investment problems in power systems using the adaptive robust optimization framework and modifications to the column-and-constraint-generation algorithm (CCGA). The first paper addresses the security-constrained short-term scheduling problem where automatic primary response is considered. A two-stage robust model is adopted, resulting in complex mixed-integer linear instances featuring binary variables associated with first- and second-stage decisions. A new tailored CCGA which explores the structure of the problem is devised. The second paper uses deep neural networks for learning the mapping of nodal demands onto generators set point for the first paper s model. Robust-based modeling approaches and the CCGA are used to enforce feasibility for the solution. This method results in important computational gains as compared to results of the first paper. The third paper proposes an adaptive data-driven approach for a two-stage robust unit commitment model, where the polyhedral uncertainty set is characterized directly from data, through the convex hull of a set of previously observed non-dispatchable generation profiles. The resulting problem is suitable for the exact CCGA. The fourth paper proposes an adaptive two-stage distributionally robust transmission expansion model incorporating long- and short-term uncertainties. A novel extended CCGA is devised to tackle distributionally robust subproblems. Finally, under a different and higher-level perspective, the fifth paper investigates the adequacy of systematic inducement prizes for fostering innovations in theoretical and computational aspects for various modern power systems challenges.