Mathematical foundations for energy networks: buffering, storage and transmission

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.

The beneficiaries of the proposed research are: Owners of generation schemes. The proposed research has the potential to increase the capacity and energy yield possible from future generation schemes, especially wind, through the optimal design and operation of future networks including storage. Transmission system operators and distribution network operators. The proposed research has the potential to make a significant contribution to the transition to a lower carbon electricity industry as well as identifying techniques which can be used to improve the efficiency and utilisation of existing and future electrical network assets without compromising the quality and security of supply. Power equipment manufacturers. The proposed research will assist with the development of rigorous business cases for emerging products, such as storage, and also provide valuable information which can be used by equipment manufacturers to direct and prioritise future R&D activities. The public sector and regulatory bodies. The proposed research should contribute to the debate regarding the most effective regulatory mechanisms in terms of supporting and enabling Smart Grid technologies and operating regimes. Industry in general and the wider public. The proposed research has the potential to lead to lower electricity prices as the buffering and storage analysis carried out could lead to a more efficient use of the existing network, the deferral or avoidance of costly network reinforcement and more cost effective, less capital intensive, new infrastructure projects. The academic community. The research will identify and develop new mathematical techniques and apply them to emerging energy networks and network technologies. This will stimulate and contribute to the academic community relating to mathematics and energy networks.