Risk-Averse Model Predictive Operation Control of Islanded Microgrids

In this paper we present a risk-averse model predictive control (MPC) scheme for the operation of islanded microgrids with very high share of renewable energy sources. The proposed scheme mitigates the effect of errors in the determination of the probability distribution of renewable infeed and load. This allows to use less complex and less accurate forecasting methods and to formulate low-dimensional scenario-based optimisation problems which are suitable for control applications. Additionally, the designer may trade performance for safety by interpolating between the conventional stochastic and worst-case MPC formulations. The presented risk-averse MPC problem is formulated as a mixed-integer quadratically-constrained quadratic problem and its favourable characteristics are demonstrated in a case study. This includes a sensitivity analysis that illustrates the robustness to load and renewable power prediction errors

Novel Optimization Approaches for Integrated Design and Operation of Smart Manufacturing and Energy Systems

This dissertation contributes novel theoretical results that enable the use of efficient optimization algorithms for the design of energy and manufacturing systems with high operational flexibility. Operational flexibility is a central theme of the smart grid and smart manufacturing paradigms because it enables systems to optimally adapt to highly dynamic and uncertain operating environments. Such environments are increasingly prevalent in the energy and manufacturing industries due to factors such as the increasing use of variable renewable energy resources (e.g., wind and solar) and the potential benefits of responding quickly to variations in product demands, real-time electricity markets, etc. For systems such as microgrids, combined heat and power plants, multiproduct chemical plants, and biorefineries, such flexibility has the potential to provide huge economic and environmental benefits. However, it also requires systems to make substantial changes in their operating conditions over very short-time scales, including discrete changes in their operating modes of process equipment (e.g., on/off) or the portfolio of products being produced. Designing systems with such operational flexibility requires consideration of the short-term operational details (e.g., minutes to hours) and future uncertainties that will affect system\u27s performance over its entire lifetime (e.g., decades). This gives rise to a complex optimization problem called integrated design and operation under uncertainty. This problem is complex mainly because the long-term design decisions of interest are tightly coupled with a very large number of short-term operational decisions that must be made over many operational periods and under significant uncertainty. Moreover, these operational decision are mixed-integer decisions, which are particularly challenging for optimization, because they are used to model both discrete and continuous changes in operations. Unfortunately, such problems cannot be solved both accurately and efficiently by standard mathematical programming approaches without major simplifications. At the same time, simplifications that are computationally tractable significantly reduce the level of operational detail that can be captured by the optimization model, which often result in system designs that are sub-optimal or even infeasible for real operations. An alternative approach, which we refer to as the simulation-based optimization (SO) approach, is to evaluate candidate system designs using a stochastic simulation of the system’s operations over all operational periods and in multiple uncertain scenarios. The design problem is then solved by optimizing the output of this simulation with respect to the design decisions. This approach is scalable to models with much more operational detail in terms of the number of operational periods and the number of uncertain scenarios considered, both of which are essential for representing operational flexibility. However, this approach results in highly complex and discontinuous optimization problems due to the discrete decisions that are made within the simulation to represent short-term operations. Hence, solving this formulation usually requires heuristic gradient-free optimization algorithms that are extremely inefficient for high-dimensional problems and offer no theoretical guarantee of finding an optimal design. To address these challenges, this dissertation presents novel theoretical results that enable the SO formulation to be solved much more efficiently using gradient-based local optimization algorithms. In contrast to the common practice of approximating the cost function as a finite sum of costs associated with discrete uncertain scenarios (i.e., sample-average approximation), we instead model the cost as the true expected value over all possible scenarios described by a continuous probability distribution. In this context, our key insight is that averaging over uncertain scenarios is a smoothing operation, and hence this expected cost can be a smooth function of the design decisions despite the fact that sample average approximations are discontinuous. When this is true, the SO formulation can be solved efficiently using gradient-based optimization methods. In Chapter 2, we develop this approach assuming that the operational decisions within the simulation are made with a logical control policy that is specified a priori. Specifically, we consider a type of controller called an energy management policy that is in common use in microgrid simulations. We then derive and rigorously prove two sets of sufficient conditions on the energy management policy under which the expected cost of the simulation is smooth. We demonstrate that these conditions are easily verifiable and often satisfied in practical applications. Finally, we implement different gradient-based algorithms, including a custom-made stochastic gradient descent algorithm, to solve the SO formulation for a representative example problem and show that this approach significantly outperforms derivative-free algorithms in both computational speed and solution quality. In Chapter 3, we extend this approach to address a much more general mathematical programming formulation of the integrated design and operation problem called multistage stochastic programming (MSP). We argue that this general MSP formulation can be accurately approximated by making all operational decisions using a parameterized mixed-integer decision rule, which reduces the MSP to an SO problem that can be solved efficiently as in Chapter 2. We then extend the smoothness conditions developed in Chapter 2. To develop this approach, we first propose a very general class of mixed-integer decision rules that is flexible enough to approximate near-optimal operational decisions for general MSPs, and then extend the sufficient conditions developed in Chapter 2 to rigorously establish smoothness of the resulting SO approximation. The resulting sufficient conditions are significantly more general than those in Chapter 2, and therefore apply to a much larger class of problems. We then show that these conditions are often satisfied in practice, and that they can always be made to hold by randomizing the decision rule. Finally, we implement different gradient-based algorithms to solve the SO approximation for a representative example problem and show that this approach significantly outperforms derivative-free algorithms in both computational speed and solution quality. Overall, the novel theoretical results developed in this dissertation are shown to enable efficient solution of significantly larger integrated design and operation problems than could be solved by existing approaches

Bidding Strategy for Networked Microgrids in the Day-Ahead Electricity Market

In recent years, microgrids have drawn increasing attention from both academic and industrial sectors due to their enormous potential benefits to the power systems. Microgrids are essentially highly-customized small-scale power systems. Microgrids’ islanding capability enables microgrids to conduct more flexible and energy-efficient operations. Microgrids have proved to be able to provide reliable and environmental-friendly electricity to quality-sensitive or off-grid consumers. In addition, during the grid-connected operation mode, microgrids can also provide support to the utility grid. World-widely continuous microgrid deployments indicate a paradigm shift from traditional centralized large-scale systems toward more distributed and customized small-scale systems. However, microgrids can cause as many problems as it solves. More efforts are needed to address these problems caused by microgrids integration. Considering there will be multiple microgrids in future power systems, the coordination problems between individual microgrids remain to be solved. Aiming at facilitating the promotion of microgrids, this thesis investigates the system-level modeling methods for coordination between multiple microgrids in the context of participating in the market. Firstly, this thesis reviews the background and recent development of microgrid coordination models. Problems of existing studies are identified. Motivated by these problems, the research objectives and structure of this thesis are presented. Secondly, this thesis examines and compares the most common frameworks for optimization under uncertainty. An improved unit commitment model considering uncertain sub-hour wind power ramp behaviors is presented to illustrate the reformulation and solution method of optimization models with uncertainty. Next, the price-maker bidding strategy for collaborative networked microgrids is presented. Multiple microgrids are coordinated as a single dispatchable entity and participate in the market as a price-maker. The market-clearing process is modeled using system residual supply/demand price-quota curves. Multiple uncertainty sources in the bidding model are mitigated with a hybrid stochastic-robust optimization framework. What’s more, this thesis further considers the privacy concerns of individual microgrids in the coordination process. Therefore a privacy-preserving solution method based on Dantzig-Wolfe decomposition is proposed to solve the bidding problem. Both computational and economic performances of the proposed model are compared with the performances of conventional centralized coordination framework. Lastly, this thesis provides suggestions on future research directions of coordination problems among multiple microgrids

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

불확실한 독립운전 상황을 고려한 마이크로그리드 운영계획 최적화

학위논문 (석사)-- 서울대학교 대학원 : 공과대학 산업공학과, 2019. 2. 이경식.본 논문은 마이크로그리드 운영자 관점에서 불확실한 독립운전 상황에 대비한 운영계획 최적화 문제를 다룬다. 마이크로그리드는 전력 수요의 상당 부분을 상위 송전계통에 의존하기 때문에, 송전계통과의 연결이 중단되는 독립운전에 적절히 대처하지 못하였을 경우 경제적으로 상당한 손실이 발생할 수 있다. 본 연구에서는 주어진 계획기간 중 발생 가능한 독립운전 사건의 집합과 각 사건의 발생 가능성을 확률로 정의하여 이를 다단계 추계적 최적화 모형으로 제시한다. 또한, 이러한 규모가 큰 혼합 정수 최적화 모형을 풀기 위한 해법으로 다양한 2단계 벤더스 분해 기법과 분해 기반 휴리스틱을 제안한다. 실험을 통해 본 논문에서 제시한 모형이 예비력을 통해 위험 상황을 대비하는 방법과, 불확실성에 대비를 하지 않는 방법에 비해 독립운전 발생 시의 비용을 절감할 수 있음을 확인하였다. 또한, 제시한 분해 기법과 휴리스틱이 일반 해법에 비해 규모가 큰 문제에 대해 효과적임을 확인하였다.In this thesis, we consider how to optimize microgrid operators operation plans in the context of uncertain islanding events. Due to the dependence of microgrid electricity demands on the main transmission system, significant financial losses can occur if the microgrid does not cope well with islanded operation, during which it is disconnected from the transmission system. A multistage stochastic optimization model is presented in this thesis. We define the set of possible islanding events during a given planning horizon, and the probability of each event. Various two-stage Benders decomposition methods and decomposition-based heuristics are proposed to solve this large-scale mixed integer optimization model. Experiments are conducted to show that the model and strategy presented in this paper can reduce the cost of islanded operation, compared with the methods based on preparing for uncertainties by defining reserve requirements or those with no preparation for uncertainty. We also found that the proposed decomposition and heuristic techniques were effective for large-scale instances than the extensive formulation approach.Chapter 1 Introduction 1 1.1 Background 1 1.1.1 Operation Planning in Power Systems 1 1.1.2 A Microgrid 3 1.2 Problem Description 5 1.3 Literature Review 6 1.3.1 Uncertainty in the UC Problem 6 1.3.2 Uncertainties in Microgrids 8 1.4 Motivations and Contributions 11 1.5 Organization of the Thesis 12 Chapter 2 Mathematical Formulations 13 2.1 Basic Formulation with No Islanding 13 2.2 Extensive Formulation considering Islanding Uncertainty 18 Chapter 3 Decomposition Approaches & Heuristics 25 3.1 Benders Decomposition Method 28 3.2 Various Decomposition Options 33 3.3 Decomposition-based Heuristics 38 Chapter 4 Computational Analysis 39 4.1 Test Instances 39 4.2 Cost & Sensitivity Analysis 42 4.2.1 Cost Analysis 42 4.2.2 Sensitivity Analysis 45 4.3 Performance of Solution Approaches 49 Chapter 5 Conclusion 55Maste

Probabilistic Optimization Techniques in Smart Power System

Uncertainties are the most significant challenges in the smart power system, necessitating the use of precise techniques to deal with them properly. Such problems could be effectively solved using a probabilistic optimization strategy. It is further divided into stochastic, robust, distributionally robust, and chance-constrained optimizations. The topics of probabilistic optimization in smart power systems are covered in this review paper. In order to account for uncertainty in optimization processes, stochastic optimization is essential. Robust optimization is the most advanced approach to optimize a system under uncertainty, in which a deterministic, set-based uncertainty model is used instead of a stochastic one. The computational complexity of stochastic programming and the conservativeness of robust optimization are both reduced by distributionally robust optimization.Chance constrained algorithms help in solving the constraints optimization problems, where finite probability get violated. This review paper discusses microgrid and home energy management, demand-side management, unit commitment, microgrid integration, and economic dispatch as examples of applications of these techniques in smart power systems. Probabilistic mathematical models of different scenarios, for which deterministic approaches have been used in the literature, are also presented. Future research directions in a variety of smart power system domains are also presented.publishedVersio

Routing and scheduling optimisation under uncertainty for engineering applications

The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits.The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits

Short - Term Bidding Strategies for a Generation Company in the Iberian Electricity Market

La posada en marxa del Mercat Ibèric de l'Electricitat va introduir al sector elèctric espanyol un seguit de nous mecanismes de participació que han forçat els agents a renovar les seves polítiques de gestió. D'aquesta nova situació sorgeix l'oportunitat d'estudiar noves estratègies d'oferta a curt termini per a companyies de generació price-taker que participin diàriament al Mercat Ibèric de l'Electricitat. Aquestes estratègies se centraran al mercat diari, ja que és aquí on es negocia un 80% de l'electricitat que es consumeix diàriament a Espanya i on s'integren gran part de la resta de mecanismes de participació. La liberalització dels mercats elèctrics obre a noves tècniques d'optimització els problemes clàssics de gestió de l'energia. En particular, atesa la incertesa que l'existència del mercat ocasiona als preus, les tècniques de programació estocàstiques es converteixen en la forma més natural per abordar aquests problemes. Als mercats elèctrics el preu es fixa horàriament com a resultat d'un procés de casació , és a dir que quan l'agent ha d'efectuar la seva oferta desconeix el preu al qual li vindrà remunerada l'energia. Aquesta incertesa fa imprescindible l'ús de tècniques estadístiques per obtenir informació del mercat i introduir-la als models d'optimització. En aquest aspecte, una de les contribucions d'aquesta tesi és l'estudi dels preus del mercat de l'electricitat a Espanya i el seu modelat mitjançant models factorials. D'altra banda, s'hi es descriuen els nous mecanismes presents al Mercat Ibèric de l'Electricitat que afecten directament la producció física de les unitats. En particular, s'inclou el modelat detallat dels contractes de futurs físics i bilaterals i de la seva inclusió a l'oferta del mercat diari per part de les companyies de generació. Als models presentats, es tenen en compte explícitament les regles del mercat, així com les clàssiques restriccions d'operació de les unitats, tant tèrmiques com de cicle combinat. A més, es deriva i es demostra l'expressió de la funció d'oferta. Per tant, els models construïts són una eina per decidir l'assignació de les unitats, la generació dels contractes de futurs físics i bilaterals a través seu i l'oferta òptima d'una companyia de generació. Un cop s'han cobert aquests objectius, es presenta una millora dels models mitjançant la inclusió de la seqüència de mercats de molt curt termini per tal de modelar la influència que tenen en l'oferta al mercat diari. Aquests mercats es casen just abans i durant el dia en què l'energia ha de ser consumida, i això permetrà veure com la possibilitat d'augmentar els beneficis participant-hi afecta directament les estratègies d'oferta òptima del mercat diari. Els models presentats en aquest treball han estat provats amb dades reals provinents del Mercat Ibèric de l'Electricitat i d'una companyia de generació que hi opera. Els resultats obtinguts són adequats i es discuteixen al llarg del documentLa puesta en marcha del Mercado Ibérico de la Electricidad introdujo en el sector eléctrico español una serie de nuevos mecanismos de participación que han forzado a los agentes a renovar sus políticas de gestión. De esta nueva situación surge la oportunidad de estudiar nuevas estrategias de oferta para las compañías de generación. Esta tesis se enmarca en las estrategias de oferta a corto plazo para compañías de generación price-taker que participen diariamente en el Mercado Ibérico de la Electricidad. Estas estrategias se centraran en el mercado diario ya que es donde se negocia un 80% de la electricidad consumida diariamente en España y es donde se integran gran parte del resto de los mecanismos de participación. La liberalización de los mercados eléctricos permite aplicar nuevas técnicas de optimización a los problemas clásicos de gestión de la energía. En concreto, dada la incertidumbre en el precio existente en el mercado, las técnicas de programación estocástica se convierten en la forma más natural para abordar estos problemas. En los mercados eléctricos el precio se fija horariamente como resultado de un proceso de casación, es decir, cuando el agente debe efectuar sus ofertas desconoce el precio al que la energía le será pagada. Esta incertidumbre hace imprescindible el uso de técnicas estadísticas para obtener información del mercado e introducirla en los modelos de optimización. En este aspecto, una de las contribuciones de esta tesis es el estudio del precio de la electricidad en España y su modelado mediante modelos factoriales. Se describen los nuevos mecanismos presentes en el Mercado Ibérico de la Electricidad que afectan directamente a la producción física de las unidades. En particular, se incluye una modelización detallada de los contratos de futuros físicos y bilaterales y su inclusión en la oferta enviada al mercado diario por las compañías de generación. En los modelos presentados se tiene en cuenta explícitamente las reglas del mercado así como las clásicas restricciones de operación de las unidades, tanto térmicas como de ciclo combinado. La expresión de la función de oferta óptima se deriva y se demuestra. Por lo tanto, los modelos construidos son una herramienta para decidir la asignación de unidades, la generación de los contratos de futuros físicos y bilaterales a través de ellas y la oferta óptima de una compañía de generación. Una vez alcanzados estos objetivos, se presenta una mejora del modelo con la inclusión de la secuencia de mercados de muy corto plazo. El objetivo es modelar la influencia que esta tiene en la oferta al mercado diario. Estos mercados se casan justo antes y durante el día en el que la energía va a ser consumida y se verá cómo la posibilidad de aumentar los beneficios participando en ellos afecta a las estrategias de oferta óptima del mercado diario. Los modelos presentados en este trabajo se han probado con datos reales procedentes del Mercado Ibérico de la Electricidad y de una compañía de generación que opera en él. Los resultados obtenidos son adecuados y se discuten a lo largo del documento.The start-up of the Iberian Electricity Market introduced a set of new mechanisms in the Spanish electricity sector that forced the agents participating in the market to change their management policies. This situation created a great opportunity for studying the bidding strategies of the generation companies in this new framework. This thesis focuses on the short-term bidding strategies of a price-taker generation company that bids daily in the Iberian Electricity Market. We will center our bidding strategies on the day-ahead market because 80% of the electricity that is consumed daily in Spain is negotiated there and also because it is the market where the new mechanisms are integrated. The liberalization of the electricity markets opens the classical problems of energy management to new optimization approaches. Specifically, because of the uncertainty that the market produces in the prices, the stochastic programming techniques have become the most natural way to deal with these problems. Notice that, in deregulated electricity markets the price is hourly fixed through a market clearing procedure, so when the agent must bid its energy it is unaware of the price at which it will be paid. This uncertainty makes it essential to use some statistic techniques in order to obtain the information coming from the markets and to introduce it in the optimization models in a suitable way. In this aspect, one of the main contributions of this thesis has been the study the Spanish electricity price time series and its modeling by means of factor models. In this thesis, the new mechanism introduced by the Iberian Market that affects the physical operation of the units is described. In particular, it considers in great detail the inclusion of the physical futures contracts and the bilateral contracts into the day-ahead market bid of the generation companies. The rules of the market operator have been explicitly taken into account within the mathematical models, along with all the classical operational constraints that affect the thermal and combined cycle units. The expression of the optimal bidding functions are derived and proved. Therefore, the models built in this thesis provide the generation company with the economic dispatch of the committed futures and bilateral contracts, the unit commitment of the units and the optimal bidding strategies for the generation company. Once these main objectives were fulfilled, we improved the previous models with an approach to the modeling of the influence that the sequence of very short markets have on optimal day-ahead bidding. These markets are cleared just before and during the day in which the electricity will be consumed and the opportunity to obtain benefits from them changes the optimal day-ahead bidding strategies of the generation company, as it will be shown in this thesis. The entire models presented in this work have been tested using real data from a generation company and Spanish electricity prices. Suitable results have been obtained and discussed

A multistage stochastic modelling framework for the optimal operation of DER aggregators under multidimensional uncertainty using stochastic dual dynamic programming

The emerging paradigm shift towards the Smart Grid concept, has vigorously encouraged the broad deployment of distributed energy resources (DER), such as energy storage (ES) and flexible demand (FD) and renewable micro-generators, in the energy system. In deregulated power systems, the deployment of flexibility pertaining to ES and FD is associated with their efficient integration in the electricity market. However, significant participation barriers have triggered the introduction of distributed energy resources (DER) aggregators in electricity markets, which settle the necessary framework for the market realisation of their promising operational flexibility potential. The significant number and diversity of resources pertaining to the DER aggregator portfolio, combined with multiple stochastic components affecting its optimal operation demonstrate a high-dimensional stochastic problem. Existing literature focusing on the problem of the optimal operation of DER aggregators exhibits significant limitations, since two-stage stochastic formulations are adopted. In this context, this thesis proposes, analyses and evaluates a novel multistage stochastic model, where multidimensional stochasticity is efficiently considered. Suitable dimensionality reduction and decomposition techniques have been deployed to tackle the computational issues stemming from the high dimensionality of the problem. Stochastic Dual Dynamic programming (SDDP) is deployed to alleviate computational tractability problems. Autoregressive models (AR) are employed to articulate temporal and cross-variable dependencies among the stochastic variables. Two novel extensions of the traditional SDDP algorithm, where linear (i.e. AR) models are integrated in the solution process and enhance solution quality, are proposed. A simulation framework for the validation and assessment of the proposed extended SDDP models, which compares them against scenario tree formulations with different structural characteristics, is presented. Case studies demonstrate that the extended SDDP models achieve a better trade-off between solution efficiency and computational performance. Additionally, results highlight the value of strategic positioning of the DER aggregator portfolio, when limited renewable generation is available. Finally, the effect of strategic decision-making based on less accurate information is shown to be intensified when the aggregator manages a more flexible portfolio.Open Acces