*This article is part of a series celebrating the 20th birthday of the Isaac Newton Institute in Cambridge. The Institute is a place where leading mathematicians from around the world can come together for weeks or months at a time to indulge in what they like doing best: thinking about maths and exchanging ideas without the distractions and duties that come with their normal working lives. And as you'll see in our articles, what starts out as abstract mathematics scribbled on the back of a napkin can have a major impact in the real world.*

When the mathematician AK Erlang first used probability theory
to model telephone networks in the early
twentieth century he could hardly have
imagined that the science he founded would
one day help solve a most pressing global
problem: how to wean ourselves off fossil fuels
and switch to renewable energy sources. But the
unlikely convergence of the two fields lay at the
heart of the *Energy Systems Week*, which took
place at the Isaac Newton Institute in May
2010. It was part of a larger programme,
*Stochastic Processes in Communication Sciences*,
exploring how the theory of randomness can be used to solve
problems arising in the telecommunications
industry.

A mathematical understanding of stochastic
processes is essential in communications
science, because a large number of users gives
rise to an essentially random pattern of calls,
emails, or other information sending requests,
which a network has to be able to deal with.
"If we integrate renewable energies, such as
wind power, in the electricity grid, there will also be uncertainty, as we don’t know what the
wind will be doing tomorrow," explains Stan
Zachary, who co-organised the *Energy Systems
Week*. "This will make planning and scheduling
much more challenging and it will take
sophisticated mathematics to get it right."

The Isaac Newton Institute provides an ideal meeting ground for experts from different backgrounds, who may not normally have the chance to interact. "Energy systems do not traditionally fit into the world of communications science," says Frank Kelly, one of the organisers of the larger meeting on stochastic processes. "However, the powerful mathematical language developed for communication networks may have applications for this new area. The presence at the Institute of a collection of people that were interested in random processes and networks made this an ideal setting for a meeting on energy systems that reached out to industry. "

The *Energy Systems Week* attracted 93
participants including mathematicians and
engineers, as well as economists and
representatives from industry and from
regulatory bodies. They were particularly
interested in how the uncertainty of supply
from wind farms can be balanced out by
traditional power plants and how smart meters
and new energy storage devices can be used to
spread demand away from peak times to
prevent the system from overloading.

The programme heralded a new synergy between power systems engineering and economics. "These days the energy network operates as a free market," explains Zachary. "For example, whether or not a supplier can take advantage of a temporary shortfall of supply to make what some might call an excess profit depends very much on such engineering issues as the speed with which a power station can be started up. There is an unusual interaction here between economics, mathematical game theory and engineering. The function of the Energy Systems Week was to bring together experts from these areas and I expect to see an ongoing dialogue between them."

Interdisciplinary dialogue is indeed
the most important impact of the
Energy Systems Week. Participant
Sean Meyn from the University of
Illinois has presented lectures given
at the *Energy Systems Week* to the
New England ISO, who coordinate
electricity supply in the north east
of the US and have expressed
interest in funding further research.
Meyn has also joined a team of
experts from academia and
industry to debate future energy
research policy at the US
Department of Energy (DOE).
"My interaction with researchers at
Cambridge during Energy Systems
Week has given me a great deal
more expertise and credibility to
advise the DOE," says Meyn.

Back in the UK, the *Energy Systems
Week* has led to another promising
pointer to the future: a successful application to the Engineering and
Physical Sciences Research Council
for a grant totalling nearly £1
million. The grant has been
awarded to Frank Kelly at the
University of Cambridge, Phillip
Taylor at Durham University and
Serguei Foss at Heriot-Watt
University and will support joint
research at the three institutions
into the mathematical foundations
of energy networks, focusing on
buffering, energy storage and
transmission. There have also been
initial exploratory discussions with
the National Grid.

Such large-scale projects spanning several disciplines require the time and space for experts to interact, and this is what the Isaac Newton Institute can provide. "Everyone who enters the Institute feels suddenly distanced from their day-to-day lives and able to fully engage with others," says Kelly. "The Institute provides a way of getting a critical mass of people together who can then concentrate on the problems in the area."

*This content now forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here. *

*
The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more. *