A Stochastic Dynamic Programming Approach To Balancing Wind Intermittency With Hydropower

Hydropower is a rapid response energy source and thus a perfect complement to the intermittency of wind power. However, the effect wind energy has on conventional hydropower systems can be felt, especially if the system is subject to several other environmental and non-power use constraints. The goal of this paper is to develop a general method for optimizing short-term hydropower operations of a realistic multireservoir hydropower system in a deregulated market setting when there is a stochastic wind input. The approach used is a modification of stochastic dynamic programming (SDP). The methodology is applied to a representation of multiple projects in the Federal Columbia River Power System, which is currently being dispatched by the Bonneville Power Administration. Currently, studies on hydropower operations optimization with wind have involved linear programming orstochastic programming, which are based on linearity of the objective function and constraints. SDP, by contrast, is a stochastic optimization method that does not require assumptions of linearity of the objective function or the constraints. The true adaptive and stochastic nonlinear formulation of the objective function can be applied to multiple timesteps, and is efficient for many timesteps compared to stochastic programming

Sequential Design for Optimal Stopping Problems

We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the stopping strategy. Namely, we introduce adaptive generation of the stochastic grids anchoring the simulated sample paths of the underlying state process. This allows for active learning of the classifiers partitioning the state space into the continuation and stopping regions. To this end, we examine sequential design schemes that adaptively place new design points close to the stopping boundaries. We then discuss dynamic regression algorithms that can implement such recursive estimation and local refinement of the classifiers. The new algorithm is illustrated with a variety of numerical experiments, showing that an order of magnitude savings in terms of design size can be achieved. We also compare with existing benchmarks in the context of pricing multi-dimensional Bermudan options.Comment: 24 page

Representation Of Uncertainty And Corridor Dp For Hydropower Optimization

This thesis focuses on optimization techniques for multi-reservoir hydropower systems operation, with a particular concern with the representation and impact of uncertainty. The thesis reports on three research investigations: 1) examination of the impact of uncertainty representations, 2) efficient solution methods for multi-reservoir stochastic dynamic programming (SDP) models, and 3) diagnostic analyses for hydropower system operation. The first investigation explores the value of sophistication in the representation of forecast and inflow uncertainty in stochastic hydropower optimization models using a sampling SDP (SSDP) model framework. SSDP models with different uncertainty representation ranging in sophistication from simple deterministic to complex dynamic stochastic models are employed when optimize a single reservoir systems [similar to Faber and Stedinger, 2001]. The effect of uncertainty representation on simulated system performance is examined with varying storage and powerhouse capacity, and with random or mean energy prices. In many cases very simple uncertainty models perform as well as more complex ones, but not always. The second investigation develops a new and efficient algorithm for solving multi-reservoir SDP models: Corridor SDP. Rather than employing a uniform grid across the entire state space, Corridor SDP efficiently concentrates points in where the system is likely to visit, as determined by historical operations or simulation. Radial basis functions (RBFs) are used for interpolation. A greedy algorithm places points where they are needed to achieve a good approximation. In a four-reservoir test case, Corridor DP achieves the same accuracy as spline-DP and linear-DP with approximately 1/10 and 1/1100 the number of discrete points, respectively. When local curvature is more pronounced (due to minimum-flow constraints), Corridor DP achieves the same accuracy as spline-DP and linear-DP with approximately 1/30 and 1/215 the number of points, respectively. The third investigation explores three diagnostic approaches for analyzing hydropower system operation. First, several simple diagnostic statistics describe reservoir volume and powerhouse capacity in units of time, allowing scale-invariant comparisons and classification of different reservoir systems and their operation. Second, a regression analysis using optimal storage/release sequences identifies the most useful hydrologic state variables . Finally spectral density estimation identifies critical time scales for operation for several single-reservoir systems considering mean and random energy prices. Deregulation of energy markets has made optimization of hydropower operations an active concern. Another development is publication of Extended Streamflow Forecasts (ESP) by the National Weather Service (NWS) and others to describe flow forecasts and their precision; the multivariate Sampling SDP models employed here are appropriately structured to incorporate such information in operational hydropower decisions. This research contributes to our ability to structure and build effective hydropower optimization models

COMPUTATIONALLY EFFICIENT HYDROPOWER OPERATIONS OPTIMIZATION FOR LARGE CASCADED HYDROPOWER SYSTEMS REFLECTING MARKET POWER, FISH CONSTRAINTS, MULTI-TURBINE POWERHOUSES, AND RENEWABLE RESOURCE INTEGRATION

Hydropower generation, though a centuries-old technology, is gaining new relevance as a way to integrate renewable energy sources to the power grid. This dissertation describes the development of efficient models for optimizing hydropower operations to address the competing priorities of renewable generation integration, economically efficient hydropower generation, and environmental stewardship, while still being able to maximize the value of wind and hydropower generation. The models are demonstrated using the 10-reservoir Federal Columbia River Power System in the Pacific Northwest in the U.S.A. Our computationally efficient nonlinear optimization model for the 10-reservoir system employs variable time step lengths and precomputed powerhouse functions and operating rules. Having shorter 8-hour time steps in the first few days of the model then transitioning to a coarser 24-hour time step for flow routing in the later stages results in optimization runtimes being decreased to 1/3rd to 1/6th of the time it takes to run the optimization with all 8-hour time steps. Our powerhouse functions reduced the many dispatch and loading decisions for multiple turbines at a hydropower project into a powerhouse generation as a function of total flow. The nonlinear optimization model incorporates forecasted inflow, hydropower plant operation, contracted energy loads, and the hydropower utility’s interaction with wholesale energy markets. When applicable the model also includes special seasonal constraints for fish addressing specified turbine operations and upper and lower bounds on spils. The opportunity costs of meeting these environmental constraints can be estimated. Additionally, we consider the market power of a very large hydropower producer in a regional market. For an entity with market power, maximizing avoided cost will result in prices that are very similar across periods, which is the economically efficient solution. In contrast, maximizing revenue will result in prices that are not balanced across periods, which may result in monopolistic behavior. To address renewable integration, our stochastic dynamic programming and nonlinear programming model builds upon the aforementioned framework with a time decomposition approach to optimize the hourly operations of a subset of the 10-reservoir hydropower system under wind generation uncertainty. This model also includes the effect that wind generation has on market prices, in addition to the hydro utility market power. We showed how introducing increasing levels of wind generation uncertainty causes the model to hedge by decreasing its commitment to the wholesale electricity market. The model estimates the opportunity costs of providing hour-by-hour balancing of the wind generation to a wind power generation owner

Fundamentos e aplicações da metodologia de superfície de resposta

Dissertação de Mestrado em Estatística, Matemática e Computação apresentada à Universidade AbertaA otimização de processos e produtos, a caracterização do sistema e a quantificação do impacto da incerteza dos parâmetros de entrada na resposta do sistema, assumem importância cada vez maior na investigação nas mais diversas áreas da sociedade, seja pelo impacto económico seja pelas consequências que possam advir. A Metodologia de Superfície de Resposta (MSR), nas suas mais diversas abordagens, tem-se revelado uma ferramenta da maior importância nestas áreas. Desde a publicação do artigo de Box e Wilson (1951) que a metodologia foi sendo objeto do interesse de investigadores no âmbito dos fundamentos e das aplicações. Esta metodologia, na abordagem tradicional, tem um carater sequencial e em cada iteração contemplam-se três etapas: definição do planeamento experimental, ajuste do modelo e otimização. Nestas seis décadas, os planeamentos experimentais foram sendo desenvolvidos para responder às aplicações e aos objetivos, com vista a proporcionar um modelo o mais preciso possível. Os modelos utilizados para aproximar a resposta foram evoluindo dos modelos polinomiais de primeira e segunda ordem para os modelos de aprendizagem automática, passando por diferentes modelos não lineares. Os métodos de otimização passaram pelo mesmo processo de expansão da metodologia, com vista a responder a desafios cada vez mais exigentes. A este caminho não são alheios o desenvolvimento computacional e a simulação. Se no início a metodologia se aplicava apenas a sistemas reais, hoje, a simulação de sistemas, nas mais diversas áreas e com crescente grau de complexidade, socorre-se dos metamodelos para reduzir os custos computacionais associados. A quantificação probabilística da incerteza é um excelente exemplo da aplicação da MSR. A quantificação do impacto da incerteza nas variáveis de entrada na resposta do sistema pode ser obtida implementando a metodologia com uma abordagem estocástica. Esta forma de implementação da metodologia também permite implementar a análise de sensibilidade. Neste trabalho faz-se um levantamento dos desenvolvimentos da MSR, nas várias fases da implementação da metodologia, nas seis décadas que decorreram desde a sua introdução. Apresentam-se três aplicações: na indústria da cerâmica, na produção florestal e na área da saúde, mais especificamente no prognóstico do cancro da mama.The processes and products optimization, the system characterization and quantification of the uncertainty impact of the input parameters on the system response assume increasing importance in research in several areas of society, either by economic impact or by the consequences that may ensue. The Response Surface Methodology (RSM), in its various approaches, has proven itself to be a tool of major importance in these fields. Since the publication of the paper of Box and Wilson (1951) the methodology has been a subject of interest to researchers in the context of the fundamentals and applications. In the traditional approach, this methodology has a sequential character, and for each iteration there are three steps involved: defining the experimental design, fitting the model and optimization. In these six decades, the experimental designs have been developed to respond to the applications and objectives, in order to provide the most accurate model possible, according to the purpose. The models used to approximate the response have evolved from first and second order polynomials models to machine learning models, going through different nonlinear models. Optimization methods have gone through the same process of expansion of the methodology, in order to meet increasingly demanding challenges. And this path is not unconnected with the computational development and computer simulation. If at the beginning the methodology was applied only to real systems, today, in simulation systems, in different areas and with increasing degree of complexity, we use the metamodel to reduce the associated computational costs. The probabilistic quantification of uncertainty is an excellent example of the application of the MSR. The quantification of the input uncertainties impact in the system response can be obtained by implementing the method with a stochastic approach. This way of implementing the methodology also allows the implementation of the sensitivity analysis. In this paper we make a survey of the developments of the MSR, at various stages of the implementation of the methodology, in the six decades that have elapsed since its introduction. We present three applications: in the ceramics industry, in forestry production and in healthcare, specifically in the breast cancer prognostic