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

这项提议解决的实际问题是，在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、核能、地热)的情况下，如何管理英国的能源系统。风电是高度不可预测的--实际上是在长达12小时的交货期上随机走动--英国风电总发电量在四个小时内可能会出现25%的不可预测的变化。这是几台大型热力发电机的容量，但为这样一台发电机预热也需要四个小时。随着政府计划广泛使用风能，英国未来四个小时的可用电力供应将有史以来第一次无法预测到需求。实时会有很大的持续不确定性，气体发生器(在整个系统中只占较小的一部分)不太可能以足够快的速度来弥补任何不足。否则，能源系统必须混合使用以下几种方式：快速但低效的气体发生器；生产商和用户的能源储存；也许更频繁的停电，和/或浪费临时的电力盈余。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几乎没有考虑到不确定性，它们往往将问题简化为大量离散的容量和时间块，步长从一小时到六小时不等，而且它们还省略了许多工程约束。更详细地建模的后备工具是模拟，但我们的工作表明，这提供了一个粗略的近似，计算速度慢得令人无法接受。所需要的是假设连续时间不确定性的数学模型，可以实施复杂的工程和其他约束，并在该环境中产生最优决策。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，如果我们简单地颠倒随机游动变量的角色，从对价格建模到对物理量建模。这打开了一个庞大的工具库，用于在复杂约束下处理混合的确定性和随机物理系统。这种方法与物理工程中用于模拟确定性系统的相关(偏微分方程组)方法一样灵活，但这种新方法比相应的模拟计算快10亿倍。三年来，我们探索了这一新方法，取得了令人振奋的结果，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和随机的，但可以是物理行为简单的(如在金融领域，最复杂的物理行为往往是购买或不购买股票的二元决策)，或者是物理行为的复杂和随机，但价格行为简单(就像我们早期的模型一样，在存储系统的进出发生复杂的流动，但燃料的价格结构是确定性的。这是现实的，如果天然气是以长期合同购买的)。这项提议旨在建立对价格和实物价格都存在复杂的实时扰动的模型。这开创了数学建模的新天地，也开辟了更广泛的经济应用领域。例如，由于电力是广泛交易的，这种模型可能会为如何运营实物电力或储存工厂、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输送电力提供最佳决策提供一个统一的框架。最后，由于模型假设的连续时间框架比大多数现有交易或工程系统允许的更丰富，因此模型可能会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.