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

该提案所解决的实际问题是如何管理英国未来的能源系统，因为未来将会有更多的不可预测的能源（风能、太阳能）和不灵活的能源（生物质能、潮汐能、核能、地热能）的使用。风力发电是高度不可预测的——实际上是在12小时内的随机游走——而英国的风力发电总量在4小时内可能会不可预测地变化25%。这是几台大型热力发电机的容量，但这样的发电机也需要4个小时的预热时间。随着政府计划广泛利用风能，英国未来4小时的可用电力供应将首次比需求更难以预测。实时的不确定性将会持续存在，而且燃气发电机（只占整个系统的一小部分）不太可能足够快地弥补任何不足。否则，系统必须使用一些混合：快速斜坡但效率低下的燃气发生器；生产者和用户的能源储存，可能更频繁的停电，和/或浪费暂时的电力盈余。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很少考虑不确定性，它们倾向于将问题简化为容量和时间的大离散块，步骤从1小时到6小时不等，而且它们还忽略了许多工程约束。更详细的建模的备用工具是模拟，但我们的工作表明，这给出了一个粗略的近似值，这是不可接受的缓慢计算。我们需要的是假设连续时间不确定性的数学模型，它可以实现复杂的工程和其他约束，并在该环境中生成最佳决策。如果我们简单地把随机游走变量的角色从对价格的建模转变为对物理量的建模，金融数学就有一个现成的工具箱，可以对随机物理系统的最佳决策进行建模。这为处理复杂约束下的混合确定性和随机物理系统打开了一个巨大的工具库。这些方法与物理工程中用于模拟确定性系统的相关（偏微分）方程一样灵活，但这种新方法比相应的模拟计算快10亿倍。三年来，我们一直在探索这种新方法，并取得了可喜的成果，但到目前为止，我们接受了一个约束，即我们的模型要么在价格行为上复杂而随机，但在物理行为上简单（如在金融领域，最复杂的物理决策往往是买或不买股票的二元决策），要么在物理行为上复杂而随机，但在价格行为上简单(如在我们的早期模型中，复杂的流体流入和流出存储系统，但燃料的价格结构是确定的，如果天然气是通过长期合同购买的，这是现实的)。这个提议的目的是建立一个模型，在这个模型中，价格和实际汇率都存在复杂的实时干扰。这开辟了新的数学建模领域，也开辟了更广泛的经济应用类别。例如，由于电力被广泛交易，这些模型可能会提供一个统一的框架，用于最佳决策，包括如何运营实体电力或存储工厂，如何以及何时提前出售其产出，以及何时在市场上交易而不打算交付电力。最后，由于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，这些模型可能为改善市场的工作和效率，以及电厂和系统的物理设计和演变提供方向。

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.