Mathematical foundations for energy networks: buffering, storage and transmission

电网是一个复杂的网络系统。需求和供应必须在一分钟一分钟的基础上平衡，大规模存储的机会有限。此外，网络中的流量受物理定律的约束，因此对流量的路径几乎没有控制;发电能力通常不能立即打开或关闭;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。在今天的市场中，发电容量的供应通常是由市场力量决定的，许多相互竞争的运营商都在寻求最大化自己的回报。减少碳排放的需要导致了新的政策，这将改变电网。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范围内也常常不可预测。为了对抗这种可变性，通过动态价格引入需求响应已被提出.未来在短时间内缓冲和储存电能的潜力也很大。智能电网技术的出现将这些可能性与消费者可以灵活响应的实时价格信号的可能性结合在一起。此外，有效的短期缓冲和存储网络的可用性，以及时移需求的能力，应该有助于避免瞬时垄断（在空间或时间上局部化），这被认为是过去十年中加州放松管制的市场遇到的问题的原因之一。未来的能源电网因此对工程师和数学家提出了严峻的挑战。需要回答的问题包括：供应的地理多样性是否有助于减少波动？通过定价的需求响应是否有助于减少波动的影响？缓冲和储存在多大程度上有助于平衡供求？电力系统动态特性对易变网络的影响是什么？在这种更复杂的环境中，我们如何安排发电机组和计算可靠电网的有效储备？我们如何在这个新的世界里做更好的预测？我们建议开发数学技术来帮助回答这些问题，以衡量解决未来网络中的波动性的成本，并评估可能使用的各种形式的时间和空间转移能量的相对有效性;这将使这些措施的好处能够相互权衡。我们将在输电和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对应于通过时间移动能量，但网络通过空间移动能量的能力--由其连接的能力和物理定律决定--与通过时间移动能量的好处密不可分。有两个主要的相互关联的主题：（a）发展能源网络中波动性的数学：特别重要的是建立一种有效容量的计算方法，以测量在一系列时间和空间尺度上表现出波动性的流量所需的容量，并确定在网络运行中至关重要的时间和空间尺度;以及（B）发展先进的概率技术来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，并为竞争的供应商、运营商和消费者设计定价和激励方案，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.