School of Engineering


Mathematical foundations for energy networks: buffering, storage and transmission

This EPSRC project is being led by the University of Durham, with a work package being carried out at Newcastle University.

Electrical power grids are complex networked systems. Demand and supply must be balanced on a minute-by-minute basis and there are limited opportunities for large-scale storage. Further, flows in networks are subject to the laws of physics, so that there is very little control over the routing of flows; generating capacity can no tin general be instantly switched on or off; sources of generation capacity, whether renewable or nuclear, are often located far from the urban and industrial areas they must serve.

In today's market, the provision of generation capacity is typically determined by market forces in which many competing operators each seek to optimize their own returns. The need to reduce carbon emissions has led to new policy which will transform the grid. Notably, renewable sources such as wind power produce supplies which are highly variable and often unpredictable, even on relatively short time scales. To combat this variability, the introduction of demand response through dynamic prices has been proposed. There is also significant future potential for the buffering and storage of electrical energy over short time scales.

These possibilities are integrated through the advent of smart grid technology, with the possibility of real-time price signaling to which consumers may respond flexibly. Further, the availability to the network of significant short-term buffering and storage, along with the ability to time-shift demand, should assist in the avoidance of transient monopolies (localised in space or time) which is considered to be one of the reasons for the problems encountered in the deregulated market in California in the last decade.

The energy grid of the future thus poses formidable challenges for engineers and mathematicians. Among the questions to be answered are:

We propose to develop mathematical techniques to assist in answering these questions, to measure the costs of addressing the volatilities in future networks, and to assess the comparative effectiveness of the various forms of time- and space-shifting of energy which may be used; this will then enable the benefits of such measures to be traded against each other. We shall develop these techniques in the context of the transmission and distribution networks: while buffering, storage and the time-shifting of demand all correspond to moving energy through time, the ability of the network to move energy through space - determined by the capacities in its links and the laws of physics - is inextricably linked to the benefits of moving energy through time.

There are two major and interlinked themes:

  1. the development of the mathematics of volatility in energy networks: of particular importance here is the creation of a calculus of effective capacities, for measuring capacity required by flows exhibiting volatility on a range of time- and space-scales, and for determining those time- and space-scales which are of critical importance in the operation of a network
  2. the development of advanced probabilistic techniques for measuring the effects of extreme events in networks.

These two themes together provide the results necessary to assess, control and optimize the performance of energy networks, and to devise the pricing and incentivisation schemes for competing suppliers, operators and consumers so as to maximise economic efficiency.