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）以及灵活的能源（生物质，潮汐，核能，地热）。风力发电是高度不可预测的-实际上是在长达12小时的交货时间内的随机游走-英国风力发电的总产量在4小时内可以不可预测地变化25%。这相当于几台大型热力发电机的发电能力，但启动这样一台发电机也需要4个小时。随着政府计划广泛使用风能，英国未来4小时的可用电力供应将首次比需求更难预测。在真实的时间内，将存在巨大的持续不确定性，并且气体发生器（其将是整个系统的较小部分）不太可能上升得足够快以补偿任何不足。否则，系统必须使用以下组合：快速上升但效率低下的天然气发电机;生产商和用户的能量存储，以及可能更频繁的停电和/或临时电力盈余的浪费。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容量和时间的大的离散块，从1小时到6小时不等，而且它们还忽略了许多工程约束。更详细地建模的后备工具是模拟，但我们的工作表明，这给出了一个粗略的近似值，计算速度慢得令人无法接受。我们需要的是数学模型，它假设连续时间的不确定性，可以实现复杂的工程和其他约束，并在这种环境下产生最优决策。金融数学有一个现成的工具包，用于模拟随机物理系统的最优决策，如果我们简单地颠倒随机游走变量的角色，从模拟价格到模拟物理量。这打开了一个巨大的武器库的工具来处理复杂的约束条件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建模确定性系统的相关（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，但迄今为止，我们接受了一个约束，即我们的模型在价格行为方面可以是复杂的和随机的，但在物理行为方面可以是简单的（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）或物理行为的复杂性和随机性，但价格行为很简单（在我们早期的模型中，复杂的流量流入和流出存储系统，但具有确定的燃料价格结构，这是现实的，如果天然气是根据长期合同购买的）本建议旨在建立模型，其中价格和实际汇率都存在复杂的真实的时间扰动。这开辟了新的数学建模领域，也开辟了更广泛的经济应用领域。例如，由于电力交易广泛，这些模型可能为如何运营实体电力或存储工厂，如何以及何时远期出售其产出，以及何时在市场上进行交易而不打算提供电力的最佳决策提供统一的框架。最后，由于这些模型假定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，这些模型可以为改进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。

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.