Heriot-Watt University, Edinburgh, Scotland
School of Mathematical and Computer Sciences

PhD studentship in the mathematics of balancing energy networks under
uncertainty

Applications are invited for a 3.5 year PhD studentship to study
mathematical and statistical aspects of the control of energy networks
under uncertainty, especially that introduced by significant future
reliance on renewable energy sources.  Candidates should have a strong
mathematical background and a particular interest in probability and
statistics.

The project is jointly funded by National Grid plc, the Scottish
Funding Council, and the Energy Academy of Heriot-Watt University. 

The student will work as part of a team, based at Cambridge, Durham,
Edinburgh and Heriot-Watt Universities, investigating the mathematics
and statistics of future energy networks.  There are strong links with
the energy industry, in particular with National Grid, and the student
may expect to spend time both with National Grid and, on occasion, at
the other academic institutions involved.  Some background to the
project is given below.

The studentship is open to applicants of all nationalities.  The
successful candidate will receive an annual tax-free stipend which is
currently £13,590.

The studentship is available to start at a mutually agreed date in 2012.

Further enquiries should be addressed to one of:
Dr S Zachary ([log in to unmask])
Dr V Shneer ([log in to unmask])

For more details of the probability and statistics group at
Heriot-Watt see
http://www.macs.hw.ac.uk/research/maths/probability-stochastic-models.htm

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Project Background

Electrical power grids are complex networked systems in which demand
and supply must be balanced both on a minute-by-minute basis and with
respect to geographical location.  Temporal balancing may assisted by
storage (time-shifting of supply) and by time-shifting of demand;
however, both these possibilities have considerable costs associated
with them, and both would present substantial challenges were they to
be implemented on a significantly larger scale than at present.
Similarly geographical balancing is achieved with the aid of the
transmission grid, which also has considerable associated costs.

At present demand and supply are primarily balanced by the accurate
prediction of the former, and the scheduling of supply to match.  Some
use is made of storage, both with regard to smoothing the predictable
daily variation in demand, and to cope with sudden surges in demand or
with system failures, e.g. of generating units or transmission links.

However, the need to reduce carbon emissions and provide increased
energy security 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
timescales.  Thus in the future, if excessive costs are to be avoided,
there will be a need for a much greater reliance on both storage and
time-shifting of demand (the latter may be achieved through, for
example, the use of smart-grid technology), both to smooth out the
greater variability in supply, and to cope with its much increased
uncertainty.  Were supply to be predictable, albeit highly variable,
the necessary calculations to make the most cost-effective use of
these capabilities would be relatively straightforward, in that the
necessary programming techniques from optimization theory are well
understood.  However, the unpredictability inherent in supplies such
as wind power, means that sophisticated stochastic models, along with
their associated analysis and optimization techniques, require to be
developed.  Thus, for example, the value of scheduled storage of a
given quantity of energy over a given time period may change up or
down as that time period is approached according to the variation in
the probability that it is going to be needed.  Similar considerations
apply to the time-shifting of demand, and then the relative costs of
the various options available (storage, time-shifting, use of highly
flexible generation, etc) must be constantly traded against each
other.  Formally, the problem is one of stochastic dynamic
programming: if, for example, one proceeds in discrete time steps (of,
say 30 mins), then at each such time there is a (potentially infinite)
range of actions available, each of which adds a quantifiable expected
value to the state of the entire system and each of which has an
associated cost; the optimal decision at that time step is typically
to maximise expected value minus cost.  Further, unacceptable events,
such as the failure to be able to meet demand, may have their
probabilities constrained to be sufficiently small.

The present position is for a PhD student to work on a 3.5-year
project to develop the necessary mathematical and statistical
techniques.  This is highly challenging.  The stochastic models will
need to be tailored to the specific requirements of electrical energy
networks -- with regard to their relevance and complexity, their
dimensioning, their tractability and their applicability.  Further,
they will need to incorporate those specific features required by the
need to satisfy network constraints at all times, so that the problem
becomes that of optimizing the movement of energy through both time
and space.  The project also has interesting and important statistical
aspects, most notably the problem of characterising the value of more
accurate flows of input data, through, for example, better weather
forecasting techniques.  Finally, there is a need to understand how
the ability to time-shift both supply and demand will affect the
electricity market and will be used by its participants to evolve
balancing strategies. This again involves the development of
sophisticated mathematical techniques from probability, optimization,
game theory and microeconomics.

It is therefore suggested that the project proceed through a number of
stages: (a) the development of the mathematical techniques for
dynamically optimising storage and time-shifting of demand in the
presence of continuously evolving uncertainty; (b) the incorporation
of network constraints and other spatial considerations; (c) the
analysis of the value of better information flows; (d) the impact of
new capabilities on the market.

In order to ensure the relevance and applicability of the project, the
PhD student would, throughout the project spend periods of time at
National Grid.  The supervisors would similarly maintain a close
liaison with the company.

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