Mathematical foundations for energy networks: buffering, storage and transmission

电网是一个复杂的网络系统。需求和供应必须在每分钟的基础上保持平衡，而大规模存储的机会有限。此外，网络中的流动受物理定律的约束，因此对流动的路径几乎没有控制；发电能力一般不能立即接通或关闭；发电能力的来源，无论是可再生能源还是核能，通常都远离它们必须服务的城市和工业区。在今天的市场上，发电能力的提供通常是由市场力量决定的，在市场力量中，许多相互竞争的运营商都在寻求优化自己的回报。减少碳排放的需求导致了将改变电网的新政策。值得注意的是，风力发电等可再生能源的供应变化很大，即使在相对较短的时间尺度上也往往无法预测。为了对抗这种可变性，已经提出通过动态价格引入需求响应。在短时间内缓冲和储存电能也有重大的未来潜力。通过智能电网技术的出现，这些可能性被整合在一起，消费者可以灵活地响应实时价格信号。此外，重要的短期缓冲和存储网络的可用性，以及时移需求的能力，应该有助于避免短暂垄断（在空间或时间上局部化），这被认为是过去十年加州放松管制市场遇到问题的原因之一。因此，未来的能源网给工程师和数学家带来了巨大的挑战。需要回答的问题包括：供应的地域多样性是否有助于减少波动性？-通过定价对需求作出反应是否有助于减少波动的影响？-缓冲和储存能在多大程度上协助平衡供求？-易失性电网中电力系统动态的影响是什么？-在这种更复杂的情况下，我们如何安排发电机组并计算可靠电网的有效储备？在这个新的世界里，我们如何做更好的预测？我们建议发展数学技术来协助回答这些问题，衡量解决未来网络波动的成本，并评估可能使用的各种形式的时间和空间能量转移的相对有效性；这将使这些措施的好处能够相互交换。我们将在输配电网络的背景下发展这些技术：虽然缓冲、存储和需求的时移都与能量随时间移动相对应，但网络在空间中移动能量的能力——由其链路的容量和物理定律决定——与能量随时间移动的好处密不可分。有两个主要且相互关联的主题：(a)能源网络波动数学的发展：特别重要的是创建有效容量的演算，用于测量在时间和空间尺度范围内表现出波动的流量所需的容量，并用于确定在网络运行中至关重要的时间和空间尺度；(b)发展先进的概率技术，用于测量网络中极端事件的影响。这两个主题共同提供了评估、控制和优化能源网络性能所需的结果，并为相互竞争的供应商、运营商和消费者设计定价和激励计划，以最大限度地提高经济效率。

Electrical power grids are complex networked systems. Demand andsupply must be balanced on a minute-by-minute basis and there arelimited opportunities for large-scale storage. Further, flows innetworks are subject to the laws of physics, so that there is verylittle control over the routing of flows; generating capacity cannotin general be instantly switched on or off; sources of generationcapacity, whether renewable or nuclear, are often located far from theurban and industrial areas they must serve. In today's market theprovision of generation capacity is typically determined by marketforces in which many competing operators each seek to optimize theirown returns.The need to reduce carbon emissions has led to new policy which willtransform the grid. Notably, renewable sources such as wind powerproduce supplies which are highly variable, and often unpredictableeven on relatively short time scales. To combat this variability theintroduction of demand response through dynamic prices has beenproposed. There is also significant future potential for thebuffering and storage of electrical energy over short time scales.These possibilities are integrated through the advent of smart gridtechnology, with the possibility of real-time price signalling towhich consumers may respond flexibly. Further, the availability tothe network of significant short-term buffering and storage, alongwith the ability to time-shift demand, should assist in the avoidanceof transient monopolies (localised in space or time) which isconsidered to be one of the reasons for the problems encountered inthe deregulated market in California in the last decade.The energy grid of the future thus poses formidable challenges forengineers and mathematicians. Among the questions to be answered are:- will geographic diversity of supply help to reduce volatility?- will demand response through pricing help to reduce the impact of volatility?- to what extent can buffering and storage assist in the balancing of supply and demand?- what is the effect of power system dynamics in a volatile network?- how may we schedule generation units and calculate efficient reserves for a reliable grid in this more complex setting?- how do we do better forecasting in this new world?We propose to develop mathematical techniques to assist in answeringthese questions, to measure the costs of addressing the volatilitiesin future networks, and to assess the comparative effectiveness of thevarious forms of time- and space-shifting of energy which may be used;this will then enable the benefits of such measures to be tradedagainst each other. We shall develop these techniques in the contextof the transmission and distribution networks: while buffering,storage and the time-shifting of demand all correspond to movingenergy through time, the ability of the network to move energy throughspace - determined by the capacities in its links and the laws ofphysics - is inextricably linked to the benefits of moving energythrough time.There are two major and interlinked themes: (a) the development of themathematics of volatility in energy networks: of particular importancehere is the creation of a calculus of effective capacities, formeasuring capacity required by flows exhibiting volatility on a rangeof time- and space-scales, and for determining those time- andspace-scales which are of critical importance in the operation of anetwork; and (b) the development of advanced probabilistic techniquesfor measuring the effects of extreme events in networks. These twothemes together provide the results necessary to assess, control andoptimize the performance of energy networks, and to devise the pricingand incentivisation schemes for competing suppliers, operators andconsumers so as to maximise economic efficiency.