Energy management decisions under real-time uncertainty in both price and load

价格和负荷实时不确定下的能源管理决策

• 批准号: EP/F027842/1
• 负责人: P Duck
• 金额: $ 18.45万
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2007
• 资助国家: 英国
• 起止时间: 2007 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FF027842%2F1
• 关键词: Energy; management; decisions; under; real

The practical problem which this proposal addresses is how to manage the UK energy system in a future where there will be much more use of unpredictable energy sources (wind, solar) and also of inflexible energy sources (biomass, tidal, nuclear, geothermal). Wind power is highly unpredictable - effectively a random walk over lead times up to 12 hours - and the total UK output of wind power can vary unpredictably by 25% over four hours. This is the capacity of several large thermal generators, but it also takes four hours to warm up such a generator.With the government's planned extensive use of wind, for the first time ever the UK's available supply of power over the next four hours will be less predictable than the demand for it. There will be large continuous uncertainty in real time, and it is unlikely that gas generators (which will be a smaller part of the total system) can ramp fast enough to compensate for any shortfalls. Otherwise the system must use some mix of: fast-ramping but inefficient gas generators; energy storage by producers and users, and perhaps more frequent power outages, and/or wastage of temporary power surpluses.The energy industry has no standard mathematical tools for even addressing this problem. Conventional models for scheduling and storage make little allowance for uncertainty, and they tend to simplify the problem to large discrete chunks of capacity and time, in steps from one to six hours, and they also omit many engineering constraints. The fall-back tool for modelling in greater detail is simulation, but our work has shown that this gives a coarse approximation, which is unacceptably slow to compute. What is needed are mathematical models which assume continuous time uncertainty, can implement complex engineering and other constraints, and generate optimal decisions in that environment.Financial mathematics has a ready-made tool kit for modelling optimal decisions about stochastic physical systems, if we simply reverse the role of the random walk variable, from modelling a price to modelling a physical quantity. This opens a huge arsenal of tools for treating mixed deterministic and stochastic physical systems under complex constraints. The methods are as flexible as the related (partial differential) equations used to model deterministic systems in physical engineering, but this new approach turns out to be one billion times faster than corresponding simulation computations. For three years we have explored this new approach with promising results, but we have so far accepted a constraint that our models can be either complex and stochastic in price behaviour, but simple in physical behaviour (as in finance, where the most complex physical decision tends to be the binary one of buying or not buying a share) or complex and stochastic in physical behaviour, but simple in price behaviour (as in our early models, where complex flows take place into and out of a storage system, but with a deterministic price structure for fuel, which is realistic if gas has been bought on a long term contract).This proposal aims to build models in which there are complex real time disturbances to both prices and physical rates. This breaks new mathematical modelling ground, and also opens a wider class of economic applications. For example because electricity is widely traded, such models might offer a unified framework for optimal decisions on how to operate a physical electricity or storage plant, how and when to sell its output forward, and when to trade in the market without intending to deliver electricity. Finally, since the models assume a richer continuous time framework than most existing trading or engineering systems permit, the models may suggest directions for improving the working and efficiency of markets, and the physical design and evolution of electricity plants and systems.

该提案解决的实际问题是如何在未来管理英国能源系统，未来将更多地使用不可预测的能源（风能、太阳能）以及不灵活的能源（生物质、潮汐能、核能、地热能）。风力发电具有高度不可预测性，实际上是在长达 12 小时的交付时间内随机游走，而英国风力发电的总输出可能会在 4 小时内不可预测地变化 25%。这是几台大型火力发电机的容量，但预热这样一台发电机也需要四个小时。随着政府计划广泛使用风能，英国未来四个小时内的可用电力供应将首次比需求更难以预测。实时存在很大的连续不确定性，并且气体发生器（这将是整个系统的一小部分）不可能足够快地斜坡来补偿任何不足。否则，系统必须使用以下组合：快速升温但效率低下的气体发生器；生产者和用户的能源储存，以及可能更频繁的停电和/或临时剩余电力的浪费。能源行业甚至没有标准的数学工具来解决这个问题。传统的调度和存储模型几乎没有考虑到不确定性，它们倾向于将问题简化为大量离散的容量和时间块，从一到六个小时不等，而且它们还忽略了许多工程约束。进行更详细建模的备用工具是模拟，但我们的工作表明，这给出了粗略的近似值，计算速度慢得令人无法接受。我们需要的是假设连续时间不确定性的数学模型，可以实现复杂的工程和其他约束，并在该环境中生成最优决策。金融数学有一个现成的工具包，用于对随机物理系统的最优决策进行建模，如果我们简单地反转随机游走变量的作用，从建模价格到建模物理量。这打开了一个巨大的工具库，用于处理复杂约束下的混合确定性和随机物理系统。这些方法与物理工程中用于对确定性系统进行建模的相关（偏微分）方程一样灵活，但事实证明，这种新方法比相应的模拟计算快十亿倍。三年来，我们一直在探索这种新方法，取得了可喜的结果，但到目前为止，我们接受了一个约束，即我们的模型可以是价格行为复杂且随机，但物理行为简单（如在金融领域，最复杂的物理决策往往是购买或不购买股票的二元决策），或者物理行为复杂且随机，但价格行为简单（如在我们早期的模型中，复杂的流量进出存储系统，但具有确定性的价格结构 燃料，如果按照长期合同购买天然气，则这是现实的）。该提案旨在建立模型，其中价格和实物价格都存在复杂的实时干扰。这开辟了新的数学建模领域，也开启了更广泛的经济应用。例如，由于电力交易广泛，此类模型可能会提供一个统一的框架，以便在如何运营实体电力或存储工厂、如何以及何时远期销售其产出以及何时在不打算提供电力的情况下在市场上进行交易等方面做出最佳决策。最后，由于这些模型假设了比大多数现有交易或工程系统所允许的更丰富的连续时间框架，因此这些模型可以为改善市场的运作和效率以及发电厂和系统的物理设计和演变提出方向。